1215

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.

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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.

1215

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.

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

1215

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.

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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.

1215

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) $810.98.

B) $721.32.

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

1215

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.

1215

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.

1215

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.

1215

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

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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

1215

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.

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

1215

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.

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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.