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标题: Reading 5: The Time Value of Money-LOS e, (Part 2)习题精选 [打印本页]
作者: bmaggie    时间: 2010-4-6 14:45     标题: [2010]Session 2:-Reading 5: The Time Value of Money-LOS e, (Part 2)习题精选

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

LOS e, (Part 2): Calculate and interpret an ordinary annuity and an annuity due.

 

 

 

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)
 an ordinary annuity of 8 periods at 12%.
C)
 a lump sum discounted for 2 years, where the lump sum is the present value of 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: bmaggie    时间: 2010-4-6 14:46

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


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: bmaggie    时间: 2010-4-6 14:46

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


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

作者: bmaggie    时间: 2010-4-6 14:46

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)
 $41,577.
B)
 $36,577.
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: bmaggie    时间: 2010-4-6 14:46

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


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

作者: bmaggie    时间: 2010-4-6 14:47

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: bmaggie    时间: 2010-4-6 14:47

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)

$62,285.

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: bmaggie    时间: 2010-4-6 14:47

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)
 $924,423.70.
C)
 $1,080,000.00.

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: bmaggie    时间: 2010-4-6 14:48

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)
 87 years.
B)
 27 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: bmaggie    时间: 2010-4-6 14:48

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)
 $901,060.
B)
 $100,135.
C)
 $90,106.

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

作者: bmaggie    时间: 2010-4-6 14:49

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: bmaggie    时间: 2010-4-6 14:49

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: bmaggie    时间: 2010-4-6 14:49

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: bmaggie    时间: 2010-4-6 14:49

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)
 $50,759.
C)
 $27,461.

N = 10; I = 15; PMT = 2,500; CPT → FV = $50,759.

作者: bmaggie    时间: 2010-4-6 14:50

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


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: bmaggie    时间: 2010-4-6 14:50

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

A)
 $721.32.
B)
 $810.98.
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: bmaggie    时间: 2010-4-6 14:50

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: bmaggie    时间: 2010-4-6 14:51

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: bmaggie    时间: 2010-4-6 14:51

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: bmaggie    时间: 2010-4-6 14:51

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

$360,000

B)
$225,000 $330,000
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: zaestau    时间: 2010-4-25 00:14

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