Reading 5: The Time Value of Money-LOS e习题精选 single, 2011, interpret, ordinary, annuity

1215

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.

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PV = 10,000; I/Y = 5; N = 5; CPT → FV = 12,763.

or: 10,000(1.05)⁵ = 12,763.

1215

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.

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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

1215

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.

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FV = 10,000(1.12)³⁰ = 299,599

Using TI BAII Plus: N = 30; I/Y = 12; PV = -10,000; CPT → FV = 299,599.

1215

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.

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

or: 500(1.075)⁴ = 667.73

1215

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.

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N = 9; I/Y = 14; FV = -25,458; PMT = 0; CPT → PV = $7,828.54.

or: 25,458/1.14⁹ = 7,828.54

1215

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

A) $432.

B) $400.

C) $578.

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

or: 500/1.05³ = 431.92.

1215

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.

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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.

1215

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.

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

1215

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%.

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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).

1215

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.

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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.