Mathematics for Management -- Supplementary Electronic Materials

Quiz: Continuous Compounding

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1 With yearly compounding at \( 10 \) percent (at the end of each year) for \( 30 \) years, the future value of an initial investment of \( 2000 \) GEL is closest to

\( 34898 \) \( 40171 \) \( 164500 \) \( 328282 \)

2 With continuous compounding at \( 10 \) percent for \( 30 \) years, the future value of an initial investment of \( 2000 \) GEL is closest to

\( 34898 \) \( 40171 \) \( 164500 \) \( 328282 \)

3 In \( 3 \) years you are to receive \( 5000 \). If the interest rate were to suddenly increase, the present value of that future amount to you would

fall raise remain unchanged cannot be determined without more information

4 Assume that the interest rate is greater than zero. Which of the following cash-inflow streams should you prefer?

Year 1: \( 400 \) GEL, Year 2: \( 300 \) GEL, Year 3: \( 200 \) GEL, and Year 4: \( 100 \) GEL Year 1: \( 100 \) GEL, Year 2: \( 200 \) GEL, Year 3: \( 300 \) GEL, and Year 4: \( 400 \) GEL Year 1: \( 250 \) GEL, Year 2: \( 250 \) GEL, Year 3: \( 250 \) GEL, and Year 4: \( 250 \) GEL any of the above, since they each sum to \( 1000 \) GEL

5 You are considering investing in a zero-coupon bond that sells for \( 250 \) GEL. At maturity in \( 16 \) years it will be redeemed for \( 1 000 \) GEL. What approximate annual rate of growth does this represent?.

\( 8 \% \) \( 9 \% \) \( 12 \% \) \( 25 \% \)

6 How long would it take \( 7000 \) GEL to grow to \( 35000 \) at \( 6\% \) compounded continuously? Round your answer to the nearest tenth of a year.

\( 27.6 \) \( 27.1 \) \( 26.0 \) \( 26.8 \)

7 Find the amount of money in an account after \( 6 \) years if \( 2900 \) GEL is deposited at \( 8\% \) annual interest compounded monthly.

\( 4601.94 \) \( 4664.47 \) \( 4642.99 \) \( 4679.16 \)

8 A portfolio manager at Wall Street buys a stock for \( 50 \) USD and sells it for \( 56 \) USD after a year. The continuously compounded rate of return is closest to (by rounding to the nearest integer):

\( 9 \% \) \( 10 \% \) \( 11 \% \) \( 12 \% \)

9 You expect to deposit the following cash flows at the end of years \( 1 \) through \( 5 \): \( 1000 \) GEL; \( 4000 \) GEL, \( 9000 \) GEL, \( 5000 \) GEL, and \( 2000 \), respectively. What is the future account value at the end of year \( 6 \) if you can earn \( 10\% \) compounded annually?

\( 15633.62 \) \( 21000.00 \) \( 25178.10 \) \( 27695.91 \)

10 You are considering borrowing \( 10 000 \) GEL for \( 3 \) years at an annual interest rate of \( 6\% \). The loan agreement calls for \( 3 \) equal payments, to be paid at the end of each of the next \( 3 \) years. (Payments include both principal and interest.) The annual payment that will fully pay off (amortize) the loan is closest to

\( 2674 \) \( 2890 \) \( 3741 \) \( 4020 \)

Your grade is: __ of 10

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Solution: 1a; 2b; 3a; 4a; 5b; 6d; 7d; 8c; 9d; 10d

Here, a, b, c, d indicate the 1st, 2nd, 3rd, and 4th answer choice, respectively, for the numbered questions.