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标题: Reading 5: The Time Value of Money-LOS e习题精选 [打印本页]
作者: 1215    时间: 2011-2-28 15:01     标题: [2011]Session 2-Reading 5: The Time Value of Money-LOS e习题精选

Session 2: Quantitative Methods: Basic Concepts
Reading 5: The Time Value of Money

LOS e: Calculate and interpret the future value (FV) and present value (PV) of a single sum of money, an ordinary annuity, an annuity due, a perpetuity (PV only), and a series of unequal cash flows.

 

 

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: 1215    时间: 2011-2-28 15:03

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)
 $14,683.
B)
 $15,301.
C)
 $14,945.

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: 1215    时间: 2011-2-28 15:04

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)
 $300,000.
C)
 $299,599.

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: 1215    时间: 2011-2-28 15:04

A $500 investment offers a 7.5% annual rate of return. How much will it be worth in four years?

A)
 $892.
B)
 $650.
C)
 $668.

N = 4; I/Y = 7.5; PV = –500; PMT = 0; CPT → FV = 667.73.

or: 500(1.075)4 = 667.73

作者: 1215    时间: 2011-2-28 15:05

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: 1215    时间: 2011-2-28 15:05

Given a 5% discount rate, the present value of $500 to be received three years from today is:

A)
 $432.
B)
 $400.
C)
 $578.

N = 3; I/Y = 5; FV = 500; PMT = 0; CPT → PV = 431.92.

or: 500/1.053 = 431.92.

作者: 1215    时间: 2011-2-28 15:05

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)
 $5,931.06.
B)
 $5,875.00.
C)
 $5,949.77.

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: 1215    时间: 2011-2-28 15:06

The value in 7 years of $500 invested today at an interest rate of 6% compounded monthly is closest to:

A)
 $780.
B)
 $760.
C)
 $750.

PV = -500; N = 7 × 12 = 84; I/Y = 6/12 = 0.5; compute FV = 760.18

作者: 1215    时间: 2011-2-28 15:06

An annuity will pay eight annual payments of $100, with the first payment to be received three years from now. If the interest rate is 12% per year, what is the present value of this annuity? The present value of:

A)
 a lump sum discounted for 3 years, where the lump sum is the present value of an ordinary annuity of 8 periods at 12%.
B)
 a lump sum discounted for 2 years, where the lump sum is the present value of an ordinary annuity of 8 periods at 12%.
C)
 an ordinary annuity of 8 periods at 12%.

The PV of an ordinary annuity (calculation END mode) gives the value of the payments one period before the first payment, which is a time = 2 value here. To get a time = 0 value, this value must be discounted for two periods (years).

作者: 1215    时间: 2011-2-28 15:07

If 10 equal annual deposits of $1,000 are made into an investment account earning 9% starting today, how much will you have in 20 years?

A)
 $39,204.
B)
 $35,967.
C)
 $42,165.

Switch to BGN mode. PMT = –1,000; N = 10, I/Y = 9, PV = 0; CPT → FV = 16,560.29. Remember the answer will be one year after the last payment in annuity due FV problems. Now PV10 = 16,560.29; N = 10; I/Y = 9; PMT = 0; CPT → FV = 39,204.23. Switch back to END mode.

作者: 1215    时间: 2011-2-28 15:07

Bill Jones is creating a charitable trust to provide six annual payments of $20,000 each, beginning next year. How much must Jones set aside now at 10% interest compounded annually to meet the required disbursements?

A)
 $154,312.20.
B)
 $95,815.74.
C)
 $87,105.21.

N = 6, PMT = -$20,000, I/Y = 10%, FV = 0, Compute PV → $87,105.21.

作者: 1215    时间: 2011-2-28 15:08

What is the present value of a 12-year annuity due that pays $5,000 per year, given a discount rate of 7.5%?

A)
 $36,577.
B)
 $41,577.
C)
 $38,676.

Using your calculator: N = 11; I/Y = 7.5; PMT = -5,000; FV = 0; CPT → PV = 36,577 + 5,000 = $41,577. Or set your calculator to BGN mode and N = 12; I/Y = 7.5; PMT = -5,000; FV = 0; CPT → PV = $41,577.

作者: 1215    时间: 2011-2-28 15:09

Consider a 10-year annuity that promises to pay out $10,000 per year; given this is an ordinary annuity and that an investor can earn 10% on her money, the future value of this annuity, at the end of 10 years, would be:

A)
 $159,374.
B)
 $175,312.
C)
 $110.000.

N = 10; I/Y = 10; PMT = -10,000; PV = 0; CPT → FV = $159,374.

作者: 1215    时间: 2011-2-28 15:09

What is the present value of a 10-year, $100 annual annuity due if interest rates are 0%?

A)
 $1,000.
B)
 $900.
C)
 No solution.

When I/Y = 0 you just sum up the numbers since there is no interest earned.

作者: 1215    时间: 2011-2-28 15:09

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)
 $52,285.
B)
 $55,364.
C)
 $62,285.

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: 1215    时间: 2011-2-28 15:09

Justin Banks just won the lottery and is trying to decide between the annual cash flow payment option or the lump sum option. He can earn 8% at the bank and the annual cash flow option is $100,000/year, beginning today for 15 years. What is the annual cash flow option worth to Banks today?

A)
 $855,947.87.
B)
 $1,080,000.00.
C)
 $924,423.70.

First put your calculator in the BGN.

N = 15; I/Y = 8; PMT = 100,000; CPT → PV = 924,423.70.

Alternatively, do not set your calculator to BGN, simply multiply the ordinary annuity (end of the period payments) answer by 1 + I/Y. You get the annuity due answer and you don’t run the risk of forgetting to reset your calculator back to the end of the period setting.

OR N = 14; I/Y = 8; PMT = 100,000; CPT → PV = 824,423.70 + 100,000 = 924,423.70.

作者: 1215    时间: 2011-2-28 15:10

If an investor puts $5,724 per year, starting at the end of the first year, in an account earning 8% and ends up accumulating $500,000, how many years did it take the investor?

A)
 27 years.
B)
 87 years.
C)
 26 years.

I/Y = 8; PMT = -5,724; FV = 500,000; CPT → N = 27.

Remember, you must put the pmt in as a negative (cash out) and the FV in as a positive (cash in) to compute either N or I/Y.

作者: 1215    时间: 2011-2-28 15:10

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)
 $901,060.
C)
 $90,106.

N = 45; PMT = –2,000; PV = 0; I/Y = 8.5%; CPT → FV = $901,060.79.

作者: 1215    时间: 2011-2-28 15:11

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)
 $6,759.
B)
 $6,145.
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: 1215    时间: 2011-2-28 15:14

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)
 $887.
B)
 $1,124.
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: 1215    时间: 2011-2-28 15:15

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)
 $13,453.
B)
 $15,000.
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: 1215    时间: 2011-2-28 15:15

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: 1215    时间: 2011-2-28 15:16

Concerning an ordinary annuity and an annuity due with the same payments and positive interest rate, which of the following statements is most accurate?

A)
 The present value of the ordinary annuity is less than an annuity due.
B)
 The present value of the ordinary annuity is greater than an annuity due.
C)
 There is no relationship.

With a positive interest rate, the present value of an ordinary annuity is less than the present value of an annuity due. The first cash flow in an annuity due is at the beginning of the period, while in an ordinary annuity, the first cash flow occurs at the end of the period. Therefore, each cash flow of the ordinary annuity is discounted one period more.

作者: 1215    时间: 2011-2-28 15:16

How much would the following income stream be worth assuming a 12% discount rate?

A)
 $810.98.
B)
 $721.32.
C)
 $1,112.44.

N i FV PV
0 12 100 100.00
1 12 200 178.57
2 12 400 318.88
3 12 300 213.53
810.98

作者: 1215    时间: 2011-2-28 15:16

You borrow $15,000 to buy a car. The loan is to be paid off in monthly payments over 5 years at 12% annual interest. What is the amount of each payment?

A)
 $546.
B)
 $456.
C)
 $334.

I = 12 / 12 = 1; N = 5 × 12 = 60; PV = 15,000; CPT → PMT = 333.67.

作者: 1215    时间: 2011-2-28 15:16

An investor deposits $4,000 in an account that pays 7.5%, compounded annually. How much will this investment be worth after 12 years?

A)
 $5,850.
B)
 $9,358.
C)
 $9,527.

N = 12; I/Y = 7.5; PV = -4,000; PMT = 0; CPT → FV = $9,527.

作者: 1215    时间: 2011-2-28 15:17

An annuity will pay eight annual payments of $100, with the first payment to be received one year from now. If the interest rate is 12% per year, what is the present value of this annuity?

A)
 $1,229.97.
B)
 $556.38.
C)
 $496.76.

N = 8; I/Y = 12%; PMT = -$100; FV = 0; CPT → PV = $496.76.

作者: 1215    时间: 2011-2-28 15:17

Renee Fisher invests $2,000 each year, starting one year from now, in a retirement account. If the investments earn 8% or 10% annually over 30 years, the amount Fisher will accumulate is closest to:
8% 10%

A)
$225,000 $330,000
B)
$225,000 $360,000
C)
$245,000 $360,000

N = 30; I/Y = 8; PMT = -2,000; PV = 0; CPT FV = 226,566.42

N = 30; I/Y = 10; PMT = -2,000; PV = 0; CPT FV = 328,988.05

作者: 1215    时间: 2011-2-28 15:17

An investment offers $100 per year forever. If Peter Wallace’s required rate of return on this investment is 10%, how much is this investment worth to him?

A)
 $10,000.
B)
 $500.
C)
 $1,000.

For a perpetuity, PV = PMT ÷ I = 100 ÷ 0.10 = 1,000.

作者: 1215    时间: 2011-2-28 15:17

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)
 $1000.
C)
 $751.

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: 1215    时间: 2011-2-28 15:17

Nortel Industries has a preferred stock outstanding that pays (fixed) annual dividends of $3.75 a share. If an investor wants to earn a rate of return of 8.5%, how much should he be willing to pay for a share of Nortel preferred stock?

A)
 $31.88.
B)
 $42.10.
C)
 $44.12.

PV = 3.75 ÷ 0.085 = $44.12.

作者: 1215    时间: 2011-2-28 15:19

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)
 $1,093.
C)
 $700.

87.50 ÷ 0.125 = $700.

作者: 1215    时间: 2011-2-28 15:20

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: 1215    时间: 2011-2-28 15:20

Assuming a discount rate of 10%, which stream of annual payments has the highest present value?

A)
    $20       –$5        $20        $110
B)
 –$100    –$100    –$100    $500
C)
    $110      $20       $10         $5

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: 1215    时间: 2011-2-28 15:20

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: 1215    时间: 2011-2-28 15:21

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)
 $919.74.
B)
 $980.89.
C)
 $905.87.

200 / (1.05) + 300 / (1.05)3 + 600 / (1.05)5 = 919.74.

作者: cheifmic    时间: 2011-4-25 16:17

 thx



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