Reading 5: The Time Value of Money-LOS d习题精选 2011, interest, invested, problems, monthly

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

LOS d: Solve time value of money problems when compounding periods are other than annual.

 

 

In 10 years, what is the value of $100 invested today at an interest rate of 8% per year, compounded monthly?

A) $222.

B) $216.

C) $180.

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N = 10 × 12 = 120; I/Y = 8/12 = 0.666667; PV = –100; PMT = 0; CPT → FV = 221.96.

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If $1,000 is invested at the beginning of the year at an annual rate of 48%, compounded quarterly, what would that investment be worth at the end of the year?

A) $1,574.

B) $1,048.

C) $4,798.

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N = 1 × 4 = 4; I/Y = 48/4 = 12; PMT = 0; PV = –1,000; CPT → FV = 1,573.52.

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Given: an 11% annual rate compounded quarterly for 2 years; compute the future value of $8,000 today.

A) $8,962.

B) $9,857.

C) $9,939.

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Divide the interest rate by the number of compound periods and multiply the number of years by the number of compound periods. I = 11 / 4 = 2.75; N = (2)(4) = 8; PV = 8,000.

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Given: $1,000 investment, compounded monthly at 12% find the future value after one year.

A) $1,126.83.

B) $1,121.35.

C) $1,120.00.

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Divide the interest rate by the number of compound periods and multiply the number of years by the number of compound periods. I = 12 / 12 = 1; N = (1)(12) = 12; PV = 1,000.

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What is the maximum price an investor should be willing to pay (today) for a 10 year annuity that will generate $500 per quarter (such payments to be made at the end of each quarter), given he wants to earn 12%, compounded quarterly?

A) $6,440.

B) $11,557.

C) $11,300.

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Using a financial calculator: N = 10 × 4 = 40; I/Y = 12 / 4 = 3; PMT = -500; FV = 0; CPT → PV = 11,557.

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An investor invested $10,000 into an account five years ago. Today, the account value is $18,682. What is the investor's annual rate of return on a continuously compounded basis?

A) 12.50%.

B) 11.33%.

C) 13.31%.

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ln(18,682/10,000) = 0.6250/5 = 12.50%

or

(18,682/10,000)^1/5 = 1.133143
ln(1.133143) = 12.4995%

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If a $45,000 car loan is financed at 12% over 4 years, what is the monthly car payment?

A) $1,185.

B) $985.

C) $1,565.

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N = 4 × 12 = 48; I/Y = 12/12 = 1; PV = –45,000; FV = 0; CPT → PMT = 1,185.02

cheifmic

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