Q1. 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 2 years, where the lump sum is the present value of an ordinary annuity of 8 periods at 12%.

B)   a lump sum discounted for 3 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%.

Q2. 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.

Q3. 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.

Q4. 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.

Q5. 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)   $159,374.

C)   $110.000.

[此贴子已经被作者于2008-12-29 17:04:23编辑过]

答案和详解如下：

Q1. 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 2 years, where the lump sum is the present value of an ordinary annuity of 8 periods at 12%.

B)   a lump sum discounted for 3 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%.

Correct answer is A)

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).

Q2. 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.

Correct answer is C)

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.

Q3. 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.

Correct answer is A)

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

Q4. 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.

Correct answer is B)

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.

Q5. 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)   $159,374.

C)   $110.000.

Correct answer is B)

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

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