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标题: Quantitative Methods 【Reading 5】Sample [打印本页]
作者: karoliukas    时间: 2012-3-22 11:13     标题: [2012 L1] Quantitative Methods 【Session 2 - Reading 5】Sample

Which one of the following statements best describes the components of the required interest rate on a security?
A)
The nominal risk-free rate, the expected inflation rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.
B)
The real risk-free rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.
C)
The real risk-free rate, the expected inflation rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.


The required interest rate on a security is made up of the nominal rate which is in turn made up of the real risk-free rate plus the expected inflation rate. It should also contain a liquidity premium as well as a premium related to the maturity of the security.
作者: karoliukas    时间: 2012-3-22 11:13

T-bill yields can be thought of as:
A)
nominal risk-free rates because they contain an inflation premium.
B)
nominal risk-free rates because they do not contain an inflation premium.
C)
real risk-free rates because they contain an inflation premium.


T-bills are government issued securities and are therefore considered to be default risk free. More precisely, they are nominal risk-free rates rather than real risk-free rates since they contain a premium for expected inflation.
作者: karoliukas    时间: 2012-3-22 11:13

The real risk-free rate can be thought of as:
A)
exactly the nominal risk-free rate reduced by the expected inflation rate.
B)
approximately the nominal risk-free rate reduced by the expected inflation rate.
C)
approximately the nominal risk-free rate plus the expected inflation rate.


The approximate relationship between nominal rates, real rates and expected inflation rates can be written as:

Nominal risk-free rate = real risk-free rate + expected inflation rate.

Therefore we can rewrite this equation in terms of the real risk-free rate as:

Real risk-free rate = Nominal risk-free rate – expected inflation rate

The exact relation is: (1 + real)(1 + expected inflation) = (1 + nominal)
作者: karoliukas    时间: 2012-3-22 11:14

A local bank offers an account that pays 8%, compounded quarterly, for any deposits of $10,000 or more that are left in the account for a period of 5 years. The effective annual rate of interest on this account is:
A)
4.65%.
B)
9.01%.
C)
8.24%.


(1 + periodic rate)m − 1 = (1.02)4 − 1 = 8.24%.
作者: karoliukas    时间: 2012-3-22 11:14

Which of the following is the most accurate statement about stated and effective annual interest rates?
A)
The stated rate adjusts for the frequency of compounding.
B)
So long as interest is compounded more than once a year, the stated annual rate will always be more than the effective rate.
C)
The stated annual interest rate is used to find the effective annual rate.


The effective annual rate, not the stated rate, adjusts for the frequency of compounding. The nominal, stated, and stated annual rates are all the same thing.
作者: karoliukas    时间: 2012-3-22 11:14

A major brokerage house is currently selling an investment product that offers an 8% rate of return, compounded monthly. Based on this information, it follows that this investment has:
A)
an effective annual rate of 8.00%.
B)
a periodic interest rate of 0.667%.
C)
a stated rate of 0.830%.


Periodic rate = 8.0 / 12 = 0.667. Stated rate is 8.0% and effective rate is 8.30%.
作者: karoliukas    时间: 2012-3-22 11:15

Use a stated rate of 9% compounded periodically to answer the following three questions. Select the choice that is the closest to the correct answer.The semi-annual effective rate is:
A)
9.00%.
B)
9.20%.
C)
9.31%.

First, we need to calculate the periodic rate, or 0.09 / 2 = 0.045.
Then, the effective semi-annual rate = (1 + 0.045)2 − 1 = 0.09203, or 9.20%.
The quarterly effective rate is:
A)
9.40%.
B)
9.00%.
C)
9.31%.

First, we need to calculate the periodic rate, or 0.09 / 4 = 0.0225.
Then, the effective annual rate = (1 + 0.0225)4 − 1 = 0.09308, or 9.31%.
The continuously compounded rate is:
A)
9.67%.
B)
9.20%.
C)
9.42%.

The continuously compounded rate = er − 1 = e0.09 − 1 = 0.09417, or 9.42%.
Calculator Keystrokes for et: Using the TI BA, enter [0.09] [2nd] [ex] (this is the key with LN on the face of the button). On the HP, enter [0.09] [g] [ex] (this key is located in blue on the key with 1/x in white print).
作者: karoliukas    时间: 2012-3-22 11:15

What’s the effective rate of return on an investment that generates a return of 12%, compounded quarterly?
A)
12.55%.
B)
14.34%.
C)
12.00%.


(1 + 0.12 / 4)4 − 1 = 1.1255 − 1 = 0.1255.
作者: karoliukas    时间: 2012-3-22 11:16

Peter Wallace wants to deposit $10,000 in a bank certificate of deposit (CD). Wallace is considering the following banks:  Which bank offers the highest effective interest rate and how much?
A)
Bank A, 5.85%.
B)
Bank C, 5.87%.
C)
Bank B, 5.90%.


Effective interest rates:
Bank A = 5.85 (already annual compounding)
Bank B, nominal = 5.75; C/Y = 12; effective = 5.90
Bank C, nominal = 5.70, C/Y = 365; effective = 5.87
Hence Bank B has the highest effective interest rate.
作者: karoliukas    时间: 2012-3-22 11:16

A local loan shark offers 4 for 5 on payday. What it involves is that you borrow $4 from him and repay $5 on the next payday (one week later). What would the stated annual interest rate be on this loan, with weekly compounding? Assuming 52 weeks in one year, what is the effective annual interest rate on this loan? Select the respective answer choices closest to your numbers.
A)
25%; 1,300%.
B)
25%; 300%.
C)
1,300%; 10,947,544%.


Stated Weekly Rate= 5/4 − 1 = 25%
Stated Annual Rate = 1,300%
Annual Effective Interest Rate = (1 + 0.25)52 − 1 = 109,476.44 − 1 = 10,947,544%
作者: karoliukas    时间: 2012-3-22 11:16

What is the effective annual rate if the stated rate is 12% compounded quarterly?
A)
57.35%.
B)
12.55%.
C)
12.00%.


EAR = (1 + 0.12 / 4)4 – 1 = 12.55%
作者: karoliukas    时间: 2012-3-22 11:17

As the number of compounding periods increases, what is the effect on the annual percentage rate (APR) and the effective annual rate (EAR)?
A)
APR increases, EAR increases.
B)
APR remains the same, EAR increases.
C)
APR increases, EAR remains the same.


The APR remains the same since the APR is computed as (interest per period) × (number of compounding periods in 1 year). As the frequency of compounding increases, the interest rate per period decreases leaving the original APR unchanged. However, the EAR increases with the frequency of compounding.
作者: karoliukas    时间: 2012-3-22 11:17

A local bank advertises that it will pay interest at the rate of 4.5%, compounded monthly, on regular savings accounts. What is the effective rate of interest that the bank is paying on these accounts?
A)
4.59%.
B)
4.65%.
C)
4.50%.


(1 + 0.045 / 12)12 − 1 = 1.0459 − 1 = 0.0459.
作者: karoliukas    时间: 2012-3-22 11:17

As the number of compounding periods increases, what is the effect on the EAR? EAR:
A)
increases at a decreasing rate.
B)
increases at an increasing rate.
C)
does not increase.


There is an upper limit to the EAR as the frequency of compounding increases. In the limit, with continuous compounding the EAR = eAPR –1. Hence, the EAR increases at a decreasing rate.
作者: karoliukas    时间: 2012-3-22 11:18

In 10 years, what is the value of $100 invested today at an interest rate of 8% per year, compounded monthly?
A)
$222.
B)
$216.
C)
$180.


N = 10 × 12 = 120; I/Y = 8/12 = 0.666667; PV = –100; PMT = 0; CPT → FV = 221.96.
作者: karoliukas    时间: 2012-3-22 11:18

If $1,000 is invested at the beginning of the year at an annual rate of 48%, compounded quarterly, what would that investment be worth at the end of the year?
A)
$1,574.
B)
$1,048.
C)
$4,798.


N = 1 × 4 = 4; I/Y = 48/4 = 12; PMT = 0; PV = –1,000; CPT → FV = 1,573.52.
作者: karoliukas    时间: 2012-3-22 11:18

Given: an 11% annual rate compounded quarterly for 2 years; compute the future value of $8,000 today.
A)
$8,962.
B)
$9,939.
C)
$9,857.


Divide the interest rate by the number of compound periods and multiply the number of years by the number of compound periods. I = 11 / 4 = 2.75; N = (2)(4) = 8; PV = 8,000.
作者: mouse123    时间: 2012-3-22 11:28

If $2,500 were put into an account at the end of each of the next 10 years earning 15% annual interest, how much would be in the account at the end of ten years?
A)
$41,965.
B)
$27,461.
C)
$50,759.


N = 10; I = 15; PMT = 2,500; CPT → FV = $50,759.
作者: mouse123    时间: 2012-3-22 11:28

An investor will receive an annuity of $5,000 a year for seven years. The first payment is to be received 5 years from today. If the annual interest rate is 11.5%, what is the present value of the annuity?
A)
$15,000.
B)
$13,453.
C)
$23,185.


With PMT = 5,000; N = 7; I/Y = 11.5; value (at t = 4) = 23,185.175. Therefore, PV (at t = 0) = 23,185.175 / (1.115)4 = $15,000.68.
作者: mouse123    时间: 2012-3-22 11:28

What is the present value of a 10-year, $100 annual annuity due if interest rates are 0%?
A)
$900.
B)
$1,000.
C)
No solution.


When I/Y = 0 you just sum up the numbers since there is no interest earned.
作者: mouse123    时间: 2012-3-22 11:29

A firm is evaluating an investment that promises to generate the following annual cash flows:
End of YearCash Flows
1$5,000
2$5,000
3$5,000
4$5,000
5$5,000
6-0-
7-0-
8$2,000
9$2,000

Given BBC uses an 8% discount rate, this investment should be valued at:
A)
$19,963.
B)
$22,043.
C)
$23,529.


PV(1 - 5): N = 5; I/Y = 8; PMT = -5,000; FV = 0; CPT → PV = 19,963
PV(6 - 7): 0
PV(8): N = 8; I/Y = 8; FV = -2,000; PMT = 0; CPT → PV = 1,080
PV(9): N = 9; I/Y = 8; FV = -2,000; PMT = 0; CPT → PV = 1,000
Total PV = 19,963 + 0 + 1,080 + 1,000 = 22,043.
作者: mouse123    时间: 2012-3-22 11:29

Compute the present value of a perpetuity with $100 payments beginning four years from now. Assume the appropriate annual interest rate is 10%.
A)
$683.
B)
$751.
C)
$1000.


Compute the present value of the perpetuity at (t = 3). Recall, the present value of a perpetuity or annuity is valued one period before the first payment. So, the present value at t = 3 is 100 / 0.10 = 1,000. Now it is necessary to discount this lump sum to t = 0. Therefore, present value at t = 0 is 1,000 / (1.10)3 = 751.
作者: mouse123    时间: 2012-3-22 11:29

Suppose you are going to deposit $1,000 at the start of this year, $1,500 at the start of next year, and $2,000 at the start of the following year in an savings account. How much money will you have at the end of three years if the rate of interest is 10% each year?
A)
$4,000.00.
B)
$5,750.00.
C)
$5,346.00.


Future value of  $1,000 for 3 periods at 10% = 1,331
Future value of $1,500 for 2 periods at 10% = 1,815
Future value of $2,000 for 1 period at 10% = 2,200
        Total = $5,346
N = 3; PV = -$1,000; I/Y = 10%; CPT → FV = $1,331
N = 2; PV = -$1,500; I/Y = 10%; CPT → FV = $1,815
N = 1; PV = -$2,000; I/Y = 10%; CPT → FV = $2,200
作者: mouse123    时间: 2012-3-22 11:30

Suppose you are going to deposit $1,000 at the start of this year, $1,500 at the start of next year, and $2,000 at the start of the following year in an savings account. How much money will you have at the end of three years if the rate of interest is 10% each year?
A)
$4,000.00.
B)
$5,750.00.
C)
$5,346.00.


Future value of  $1,000 for 3 periods at 10% = 1,331
Future value of $1,500 for 2 periods at 10% = 1,815
Future value of $2,000 for 1 period at 10% = 2,200
        Total = $5,346
N = 3; PV = -$1,000; I/Y = 10%; CPT → FV = $1,331
N = 2; PV = -$1,500; I/Y = 10%; CPT → FV = $1,815
N = 1; PV = -$2,000; I/Y = 10%; CPT → FV = $2,200
作者: mouse123    时间: 2012-3-22 11:30

Assuming a discount rate of 10%, which stream of annual payments has the highest present value?
A)
   $110      $20       $10         $5
B)
   $20       –$5        $20        $110
C)
–$100    –$100    –$100    $500


This is an intuition question. The two cash flow streams that contain the $110 payment have the same total cash flow but the correct answer is the one where the $110 occurs earlier. The cash flow stream that has the $500 that occurs four years hence is overwhelmed by the large negative flows that precede it.
作者: mouse123    时间: 2012-3-22 11:31

The following stream of cash flows will occur at the end of the next five years.

Yr 1

-2,000

Yr 2

-3,000

Yr 3

6,000

Yr 4

25,000

Yr 5

30,000


At a discount rate of 12%, the present value of this cash flow stream is closest to:
A)
$36,965.
B)
$33,004.
C)
$58,165.


N = 1; I/Y = 12; PMT = 0; FV = -2,000; CPT → PV = -1,785.71.
N = 2; I/Y = 12; PMT = 0; FV = -3,000; CPT → PV = -2,391.58.
N = 3; I/Y = 12; PMT = 0; FV = 6,000; CPT → PV = 4,270.68.
N = 4; I/Y = 12; PMT = 0; FV = 25,000; CPT → PV = 15,887.95.
N = 5; I/Y = 12; PMT = 0; FV = 30,000; CPT → PV = 17,022.81.
Sum the cash flows: $33,004.15.
Note: If you want to use your calculator's NPV function to solve this problem, you need to enter zero as the initial cash flow (CF0). If you enter -2,000 as CF0, all your cash flows will be one period too soon and you will get one of the wrong answers.
作者: mouse123    时间: 2012-3-22 11:31

If $2,000 a year is invested at the end of each of the next 45 years in a retirement account yielding 8.5%, how much will an investor have at retirement 45 years from today?
A)
$100,135.
B)
$90,106.
C)
$901,060.


N = 45; PMT = –2,000; PV = 0; I/Y = 8.5%; CPT → FV = $901,060.79.
作者: mouse123    时间: 2012-3-22 11:32

An investor wants to receive $1,000 at the beginning of each of the next ten years with the first payment starting today. If the investor can earn 10 percent interest, what must the investor put into the account today in order to receive this $1,000 cash flow stream?
A)
$6,145.
B)
$6,759.
C)
$7,145.


This is an annuity due problem. There are several ways to solve this problem.
Method 1:
PV of first $1,000 = $1,000
PV of next 9 payments at 10% = 5,759.02
Sum of payments = $6,759.02

Method 2:
Put calculator in BGN mode.
N = 10; I = 10; PMT = -1,000; CPT → PV = 6,759.02
Note: make PMT negative to get a positive PV. Don’t forget to take your calculator out of BGN mode.

Method 3:
You can also find the present value of the ordinary annuity $6,144.57 and multiply by 1 + k to add one year of interest to each cash flow. $6,144.57 × 1.1 = $6,759.02.
作者: mouse123    时间: 2012-3-22 11:32

An investor purchases a 10-year, $1,000 par value bond that pays annual coupons of $100. If the market rate of interest is 12%, what is the current market value of the bond?
A)
$1,124.
B)
$887.
C)
$950.


Note that bond problems are just mixed annuity problems. You can solve bond problems directly with your financial calculator using all five of the main TVM keys at once. For bond-types of problems the bond’s price (PV) will be negative, while the coupon payment (PMT) and par value (FV) will be positive. N = 10; I/Y = 12; FV = 1,000; PMT = 100; CPT → PV = –886.99.
作者: mouse123    时间: 2012-3-22 11:33

Given investors require an annual return of 12.5%, a perpetual bond (i.e., a bond with no maturity/due date) that pays $87.50 a year in interest should be valued at:
A)
$70.
B)
$700.
C)
$1,093.


87.50 ÷ 0.125 = $700.
作者: mouse123    时间: 2012-3-22 11:33

What is the total present value of $200 to be received one year from now, $300 to be received 3 years from now, and $600 to be received 5 years from now assuming an interest rate of 5%?
A)
$980.89.
B)
$905.87.
C)
$919.74.


200 / (1.05) + 300 / (1.05)3 + 600 / (1.05)5 = 919.74.
作者: mouse123    时间: 2012-3-22 11:33

What is the maximum an investor should be willing to pay for an annuity that will pay out $10,000 at the beginning of each of the next 10 years, given the investor wants to earn 12.5%, compounded annually?
A)
$62,285.
B)
$52,285.
C)
$55,364.

Using END mode, the PV of this annuity due is $10,000 plus the present value of a 9-year ordinary annuity: N=9; I/Y=12.5; PMT=-10,000; FV=0; CPT PV=$52,285; $52,285 + $10,000 = $62,285.
Or set your calculator to BGN mode then N=10; I/Y=12.5; PMT=-10,000; FV=0; CPT PV= $62,285.
作者: mouse123    时间: 2012-3-22 11:34

Find the future value of the following uneven cash flow stream. Assume end of the year payments. The discount rate is 12%.

Year 1

-2,000


Year 2

-3,000


Year 3

6,000


Year 4

25,000


Year 5

30,000

A)
$58,164.58.
B)
$65,144.33.
C)
$33,004.15.


N = 4; I/Y = 12; PMT = 0; PV = -2,000; CPT → FV = -3,147.04
N = 3; I/Y = 12; PMT = 0; PV = -3,000; CPT → FV = -4,214.78
N = 2; I/Y = 12; PMT = 0; PV = 6,000; CPT → FV = 7,526.40
N = 1; I/Y = 12; PMT = 0; PV = 25,000; CPT → FV = 28,000.00
N = 0; I/Y = 12; PMT = 0; PV = 30,000; CPT → FV = 30,000.00
Sum the cash flows: $58,164.58.
Alternative calculation solution: -2,000 × 1.124 − 3,000 × 1.123 + 6,000 × 1.122 + 25,000 × 1.12 + 30,000 = $58,164.58.
作者: mouse123    时间: 2012-3-22 11:34

An investor deposits $10,000 in a bank account paying 5% interest compounded annually. Rounded to the nearest dollar, in 5 years the investor will have:
A)
$12,763.
B)
$12,500.
C)
$10,210.


PV = 10,000; I/Y = 5; N = 5; CPT → FV = 12,763.
or: 10,000(1.05)5 = 12,763.
作者: mouse123    时间: 2012-3-22 11:34

If a person needs $20,000 in 5 years from now and interest rates are currently 6% how much do they need to invest today if interest is compounded annually?
A)
$14,945.
B)
$14,683.
C)
$15,301.


PV = FV / (1 + r)n = 20,000 / (1.06)5 = 20,000 / 1.33823 = $14,945
N = 5; I/Y = 6%; PMT = 0; FV = $20,000; CPT → PV = -$14,945.16
作者: mouse123    时间: 2012-3-22 11:35

What will $10,000 become in 5 years if the annual interest rate is 8%, compounded monthly?
A)
$14,693.28.
B)
$14,802.44.
C)
$14,898.46.

FV(t=5) = $10,000 × (1 + 0.08 / 12)60 = $14,898.46
N = 60 (12 × 5); PV = -$10,000; I/Y = 0.66667 (8% / 12months); CPT → FV = $14,898.46
作者: mouse123    时间: 2012-3-22 11:35

If $10,000 is invested in a mutual fund that returns 12% per year, after 30 years the investment will be worth:
A)
$10,120.
B)
$299,599.
C)
$300,000.


FV = 10,000(1.12)30 = 299,599
Using TI BAII Plus: N = 30; I/Y = 12; PV = -10,000; CPT → FV = 299,599.
作者: mouse123    时间: 2012-3-22 11:36

A $500 investment offers a 7.5% annual rate of return. How much will it be worth in four years?
A)
$892.
B)
$668.
C)
$650.


N = 4; I/Y = 7.5; PV = –500; PMT = 0; CPT → FV = 667.73.
or: 500(1.075)4 = 667.73
作者: mouse123    时间: 2012-3-22 11:36

A certain investment product promises to pay $25,458 at the end of 9 years. If an investor feels this investment should produce a rate of return of 14%, compounded annually, what’s the most he should be willing to pay for it?
A)
$9,426.
B)
$7,829.
C)
$7,618.


N = 9; I/Y = 14; FV = -25,458; PMT = 0; CPT → PV = $7,828.54.
or: 25,458/1.149 = 7,828.54
作者: mouse123    时间: 2012-3-22 11:36

Given a 5% discount rate, the present value of $500 to be received three years from today is:
A)
$400.
B)
$578.
C)
$432.


N = 3; I/Y = 5; FV = 500; PMT = 0; CPT → PV = 431.92.
or: 500/1.053 = 431.92.
作者: mouse123    时间: 2012-3-22 11:37

A local bank offers a certificate of deposit (CD) that earns 5.0% compounded quarterly for three and one half years. If a depositor places $5,000 on deposit, what will be the value of the account at maturity?
A)
$5,949.77.
B)
$5,931.06.
C)
$5,875.00.


The value of the account at maturity will be: $5,000 × (1 + 0.05 / 4)(3.5 × 4) = $5.949.77;
or with a financial calculator: N = 3 years × 4 quarters/year + 2 = 14 periods; I = 5% / 4 quarters/year = 1.25; PV = $5,000; PMT = 0; CPT → FV = $5,949.77.
作者: mouse123    时间: 2012-3-22 11:37

The value in 7 years of $500 invested today at an interest rate of 6% compounded monthly is closest to:
A)
$760.
B)
$780.
C)
$750.


PV = -500; N = 7 × 12 = 84; I/Y = 6/12 = 0.5; compute FV = 760.18
作者: mouse123    时间: 2012-3-22 11:37

Natalie Brunswick, neurosurgeon at a large U.S. university, was recently granted permission to take an 18-month sabbatical that will begin one year from today. During the sabbatical, Brunswick will need $2,500 at the beginning of each month for living expenses that month. Her financial planner estimates that she will earn an annual rate of 9% over the next year on any money she saves. The annual rate of return during her sabbatical term will likely increase to 10%. At the end of each month during the year before the sabbatical, Brunswick should save approximately:
A)
$3,356.
B)
$3,505.
C)
$3,330.


This is a two-step problem. First, we need to calculate the present value of the amount she needs over her sabbatical. (This amount will be in the form of an annuity due since she requires the payment at the beginning of the month.) Then, we will use future value formulas to determine how much she needs to save each month (ordinary annuity).
Step 1: Calculate present value of amount required during the sabbatical
Using a financial calculator: Set to BEGIN Mode, then N = 12 × 1.5 = 18; I/Y = 10 / 12 = 0.8333; PMT = 2,500; FV = 0; CPT → PV = 41,974
Step 2: Calculate amount to save each month
Make sure the calculator is set to END mode, then N = 12; I/Y = 9 / 12 = 0.75; PV = 0; FV = 41,974; CPT → PMT = -3,356
作者: mouse123    时间: 2012-3-22 11:38

John is getting a $25,000 loan, with an 8% annual interest rate to be paid in 48 equal monthly installments. If the first payment is due at the end of the first month, the principal and interest values for the first payment are closest to:
PrincipalInterest
A)
$443.65   $166.67
B)
$410.32 $200.00
C)
$443.65   $200.00


Calculate the payment first:
N = 48; I/Y = 8/12 = 0.667; PV = 25,000; FV = 0; CPT PMT = 610.32.
Interest = 0.006667 × 25,000 = $166.67; Principal = 610.32 – 166.67 = $443.65 .
作者: mouse123    时间: 2012-3-22 11:38

An individual borrows $200,000 to buy a house with a 30-year mortgage requiring payments to be made at the end of each month. The interest rate is 8%, compounded monthly. What is the monthly mortgage payment?
A)
$1,467.53.
B)
$2,142.39.
C)
$1,480.46.


With PV = 200,000; N = 30 × 12 = 360; I/Y = 8/12; CPT → PMT = $1,467.53.
作者: mouse123    时间: 2012-3-22 11:39

Marc Schmitz borrows $20,000 to be paid back in four equal annual payments at an interest rate of 8%. The interest amount in the second year’s payment would be:
A)
$6038.40.
B)
$1116.90.
C)
$1244.90.


With PV = 20,000, N = 4, I/Y = 8, computed Pmt = 6,038.42. Interest (Yr1) = 20,000(0.08) = 1600. Interest (Yr2) = (20,000 − (6038.42 − 1600))(0.08) = 1244.93
作者: mouse123    时间: 2012-3-22 11:39

It will cost $20,000 a year for four years when an 8-year old child is ready for college. How much should be invested today if the child will make the first of four annual withdrawals 10-years from today? The expected rate of return is 8%.
A)
$66,243.
B)
$33,138.
C)
$30,683.


First, find the present value of the college costs as of the end of year 9. (Remember that the PV of an ordinary annuity is as of time = 0. If the first payment is in year 10, then the present value of the annuity is indexed to the end of year 9). N = 4; I/Y = 8; PMT = 20,000; CPT → PV = $66,242.54. Second, find the present value of this single sum: N = 9; I/Y = 8; FV = 66,242.54; PMT = 0; CPT → PV = 33,137.76.
作者: andytrader    时间: 2012-3-22 12:39

An investor who requires an annual return of 12% has the choice of receiving one of the following:
Which option has the highest present value (PV) and approximately how much greater is it than the other option?
A)
Option A's PV is $42 greater than option B's.
B)
Option B's PV is $27 greater than option A's.
C)
Option B's PV is $114 greater than option A's.

Option A: N = 10, PMT = -$1,225, I = 12%, FV = 0, Compute PV = $6,921.52.
Option B: N = 9, PMT = -$1,097.96, I = 12%, FV = 0, Compute PV → $5,850.51 + 1,097.96 = 6,948.17 or put calculator in Begin mode N = 10, PMT = $1,097.96, I = 12%, FV = 0, Compute PV → $6,948.17. Difference between the 2 options = $6,921.52 − $6,948.17 = -$26.65.
Option B's PV is approximately $27 higher than option A's PV.
作者: andytrader    时间: 2012-3-22 12:39

A recent ad for a Roth IRA includes the statement that if a person invests $500 at the beginning of each month for 35 years, they could have $1,000,000 for retirement. Assuming monthly compounding, what annual interest rate is implied in this statement?
A)
7.625%.
B)
7.411%.
C)
6.988%.


Solve for an annuity due with a future value of $1,000,000, a number of periods equal to (35 × 12) = 420, payments = -500, and present value = 0. Solve for i. i = 0.61761 × 12 = 7.411% stated annually. Don’t forget to set your calculator for payments at the beginning of the periods. If you don’t, you’ll get 7.437%.
作者: andytrader    时间: 2012-3-22 12:40

Which of the following statements about compounding and interest rates is least accurate?
A)
All else equal, the longer the term of a loan, the lower will be the total interest you pay.
B)
Present values and discount rates move in opposite directions.
C)
On monthly compounded loans, the effective annual rate (EAR) will exceed the annual percentage rate (APR).


Since the proportion of each payment going toward the principal decreases as the original loan maturity increases, the total dollars interest paid over the life of the loan also increases.
作者: andytrader    时间: 2012-3-22 12:40

Elise Corrs, hedge fund manager and avid downhill skier, was recently granted permission to take a 4 month sabbatical. During the sabbatical, (scheduled to start in 11 months), Corrs will ski at approximately 12 resorts located in the Austrian, Italian, and Swiss Alps. Corrs estimates that she will need $6,000 at the beginning of each month for expenses that month. (She has already financed her initial travel and equipment costs.) Her financial planner estimates that she will earn an annual rate of 8.5% during her savings period and an annual rate of return during her sabbatical of 9.5%. How much does she need to put in her savings account at the end of each month for the next 11 months to ensure the cash flow she needs over her sabbatical? Each month, Corrs should save approximately:
A)
$2,065.
B)
$2,080.
C)
$2,070.


This is a two-step problem. First, we need to calculate the present value of the amount she needs over her sabbatical. (This amount will be in the form of an annuity due since she requires the payment at the beginning of the month.) Then, we will use future value formulas to determine how much she needs to save each month.
Step 1:  Calculate present value of amount required during the sabbatical
Using a financial calculator: Set to BEGIN Mode, then N = 4; I/Y = 9.5 / 12 = 0.79167; PMT = 6,000; FV = 0; CPT → PV = -23,719.
Step 2:  Calculate amount to save each month
Using a financial calculator: Make sure it is set to END mode, then N = 11; I/Y = 8.5 / 12.0 = 0.70833; PV = 0; FV = 23,719; CPT → PMT= -2,081, or approximately $2,080.
作者: andytrader    时间: 2012-3-22 12:40

Nikki Ali and Donald Ankard borrowed $15,000 to help finance their wedding and reception. The annual payment loan carries a term of seven years and an 11% interest rate. Respectively, the amount of the first payment that is interest and the amount of the second payment that is principal are approximately:
A)
$1,468; $1,702.
B)
$1,650; $1,468.
C)
$1,650; $1,702.


Step 1: Calculate the annual payment.
Using a financial calculator (remember to clear your registers): PV = 15,000; FV = 0; I/Y = 11; N = 7; PMT = $3,183

Step 2: Calculate the portion of the first payment that is interest.
Interest1 = Principal × Interest rate = (15,000 × 0.11) = 1,650

Step 3: Calculate the portion of the second payment that is principal.

Principal1 = Payment − Interest1 = 3,183 − 1,650 = 1,533 (interest calculation is from Step 2)
Interest2 = Principal remaining × Interest rate = [(15,000 − 1.533) × 0.11] = 1,481
Principal2 = Payment − Interest1 = 3,183 − 1,481 = 1,702
作者: andytrader    时间: 2012-3-22 12:41

How much should an investor have in a retirement account on his 65th birthday if he wishes to withdraw $40,000 on that birthday and each of the following 14 birthdays, assuming his retirement account is expected to earn 14.5%?
A)
$234,422.
B)
$274,422.
C)
$272,977.


This is an annuity due so set your calculator to the BGN mode. N = 15; I/Y = 14.5; PMT = –40,000; FV = 0; CPT → PV = 274,422.50. Switch back to END mode.
作者: andytrader    时间: 2012-3-22 12:41

Sarah Parker is buying a new $25,000 car. Her trade-in is worth $5,000 so she needs to borrow $20,000. The loan will be paid in 48 monthly installments and the annual interest rate on the loan is 7.5%. If the first payment is due at the end of the first month, what is Sarah’s monthly car payment?
A)
$483.58.
B)
$416.67.
C)
$480.57.


N = 48; I/Y = 7.5 / 12 = 0.625; PV = 20,000; FV = 0; CPT → PMT = 483.58.
作者: andytrader    时间: 2012-3-22 12:41

The First State Bank is willing to lend $100,000 for 4 years at a 12% rate of interest, with the loan to be repaid in equal semi-annual payments. Given the payments are to be made at the end of each 6-month period, how much will each loan payment be?
A)
$25,450.
B)
$32,925.
C)
$16,104.


N = 4 × 2 = 8; I/Y = 12/2 = 6; PV = -100,000; FV = 0; CPT → PMT = 16,103.59.
作者: andytrader    时间: 2012-3-22 12:42

An investor has the choice of two investments. Investment A offers interest at 7.25% compounded quarterly. Investment B offers interest at the annual rate of 7.40%. Which investment offers the higher dollar return on an investment of $50,000 for two years, and by how much?
A)
Investment B offers a $36.92 greater return.
B)
Investment A offers a $122.18 greater return.
C)
Investment A offers a $53.18 greater return.


Investment A: I = 7.25 / 4; N = 2 × 4 = 8; PV = $50,000; PMT = 0; CPT → FV = $57,726.98
Investment B: I = 7.40; N = 2; PV = $50,000; PMT = 0; CPT → FV = $57,673.80
Difference = investment A offers a $53.18 greater dollar return.
作者: andytrader    时间: 2012-3-22 12:42

Steve Hall wants to give his son a new car for his graduation. If the cost of the car is $15,000 and Hall finances 80% of the value of the car for 36 months at 8% annual interest, his monthly payments will be:
A)
$376.
B)
$413.
C)
$289.


PV = 0.8 × 15,000 = -12,000; N = 36; I = 8/12 = 0.667; CPT → PMT = 376.
作者: andytrader    时间: 2012-3-22 12:42

Lois Weaver wants to have $1.5 million in a retirement fund when she retires in 30 years. If Weaver can earn a 9% rate of return on her investments, approximately how much money must she invest at the end of each of the next 30 years in order to reach her goal?
A)
$50,000.
B)
$11,005.
C)
$28,725.


Using a financial calculator: N = 30; I/Y = 9; FV = -1,500,000; PV = 0; CPT → PMT = 11,004.52.
作者: andytrader    时间: 2012-3-22 12:43

Optimal Insurance is offering a deferred annuity that promises to pay 10% per annum with equal annual payments beginning at the end of 10 years and continuing for a total of 10 annual payments. For an initial investment of $100,000, what will be the amount of the annual payments?

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

$100,000

?

?

?

?

?

?

?

?

?

?

A)
$38,375.
B)
$25,937.
C)
$42,212.


At the end of the 10-year deferral period, the value will be: $100,000 × (1 + 0.10)10 = $259,374.25. Using a financial calculator: N = 10, I = 10, PV = $100,000, PMT = 0, Compute FV = $259,374.25. Using a financial calculator and solving for a 10-year annuity due because the payments are made at the beginning of each period (you need to put your calculator in the “begin” mode), with a present value of $259,374.25, a number of payments equal to 10, an interest rate equal to ten percent, and a future value of $0.00, the resultant payment amount is $38,374.51. Alternately, the same payment amount can be determined by taking the future value after nine years of deferral ($235,794.77), and then solving for the amount of an ordinary (payments at the end of each period) annuity payment over 10 years.
作者: andytrader    时间: 2012-3-22 12:43

Vega research has been conducting investor polls for Third State Bank. They have found the most investors are not willing to tie up their money in a 1-year (2-year) CD unless they receive at least 1.0% (1.5%) more than they would on an ordinary savings account. If the savings account rate is 3%, and the bank wants to raise funds with 2-year CDs, the yield must be at least:
A)
4.0%, and this represents a required rate of return.
B)
4.5%, and this represents a discount rate.
C)
4.5%, and this represents a required rate of return.


Since we are taking the view of the minimum amount required to induce investors to lend funds to the bank, this is best described as a required rate of return. Based upon the numerical information, the rate must be 4.5% (= 3.0 + 1.5).
作者: andytrader    时间: 2012-3-22 12:43

Selmer Jones has just inherited some money and wants to set some of it aside for a vacation in Hawaii one year from today. His bank will pay him 5% interest on any funds he deposits. In order to determine how much of the money must be set aside and held for the trip, he should use the 5% as a:
A)
required rate of return.
B)
discount rate.
C)
opportunity cost.


He needs to figure out how much the trip will cost in one year, and use the 5% as a discount rate to convert the future cost to a present value. Thus, in this context the rate is best viewed as a discount rate.
作者: andytrader    时间: 2012-3-22 12:44

Wei Zhang has funds on deposit with Iron Range bank. The funds are currently earning 6% interest. If he withdraws $15,000 to purchase an automobile, the 6% interest rate can be best thought of as a(n):
A)
opportunity cost.
B)
financing cost.
C)
discount rate.


Since Wei will be foregoing interest on the withdrawn funds, the 6% interest can be best characterized as an opportunity cost — the return he foregoes by postponing his auto purchase until the future.
作者: 影子背后    时间: 2012-4-16 18:31

请问 有没近几年的sample汇总文件啊  急！
作者: CCherrie    时间: 2012-8-17 13:39

19楼的题为什么选A不选B啊，看题中描述这个不是求Perpetuity PV啊....
作者: terpsichorefan    时间: 2013-3-12 23:47

thanks for sharing



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