Reading 5: The Time Value of Money-LOS e, (Part 2)习题精选 payments, ordinary, interpret, div, class

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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%.

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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).

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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.

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

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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.

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

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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

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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

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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.

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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.

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

• $100 received today.
• $200 received 1 year from today.
• $400 received 2 years from today.
• $300 received 3 years from today.

A) $721.32.

B) $810.98.

C) $1,112.44.

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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

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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.

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

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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.

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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.

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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.

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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.