2. Future value/Chapter 4

The principle of the time value of money is probably the single most important concept in financial management. One of the most frequently encountered applications involves the calculation of a future value.

(1) The process for converting present values to future values is referred to as _________________ .

Options: (a) discounting

(b) compounding

(2) Which of the following is not one of these variables?

(a) The interest rate (r) that could be earned by invested funds

(b) The present value (PV) of the amount invested

(c) The duration of the investment (n)

(d) The inflation rate indicating the change in average prices

All other things being equal, the numerical difference between a present and a future value corresponds to the amount of interest earned during the deposit or investment period. Each line on the following graph corresponds to an interest rate: 0%, 11%, or 22%.

Identify the interest rate that corresponds with each line.

Line A corresponds to (3) _________ , while Line B is consistent with (4) ___ . Line C corresponds to (5) ___________ . Investments and loans base their interest calculations on one of two possible methods: the (6) ___________ interest and the (7) _____________ interest methods. Both methods apply three variablesthe amount of principal, the interest rate, and the investment or deposit periodto the amount deposited or invested in order to compute the amount of interest. However, the two methods differ in their relationship between the variables.

options for problems: (3-5) 22%,11%,0%

(6) (a) complex (b) simple

(7) (a) compound (b) uncomplicated

(8) Assume that the variables r, n, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using simple interest?

(a) FV=PV+(PVrn)

(b) FV=PV1rn FV=PVIn

(c) FV=PV(PVrn)

(9) Which equation best represents the calculation of a future value (FV) using compound interest?

(a) FV=PV(1 + r)n

(b) FV=(1+r)nPV

(c) FV=PV(1 + r)n

(d) FV=PV+(PVrn)

Identify whether the following statements about the simple and compound interest methods are true or false. Mark (10-12) with True False.

(10) All other variables held constant, investments paying simple interest have to pay significantly higher interest rates to earn the same amount of interest as an account earning compound interest.

(11) All other factors being equal, when interest is paid annually, both the simple interest and the compound interest methods will generate different amounts of earned interest by the end of the first year.

(12) The process of earning compound interest allows a depositor or investor to earn interest on any interest earned in prior periods.

Cho is willing to invest $20,000 for nine years, and is an economically rational investor. She has identified three investment alternatives (L, M, and P) that vary in their method of calculating interest and in the annual interest rate offered.

Since she can only make one investment during the nine-year investment period, complete the following table and indicate whether Cho should invest in each of the investments.

Note: When calculating each investments future value, assume that all interest is compounded annually. The final value should be rounded to the nearest whole dollar.

Investment Interest rate and Method Expected future value Make this investment?

L 5% compound interest (13) _____________ (14) _____

M 4% simple interest (15) _____________ (16) _____

P 7% compound interest (17) _____________ (18) _____

options for problems (13) $31,027, $26,095, $34,400 (15) $34,400, $26,095, $27,200

(17) $36,769,$26,095,$34,400

(14), (16), (18) option yes or no

(?) 20000 15000 B DOLLARS (PV) 10000 5000 O + + +> 10 0 1 2 3 4 7 8 9 5 6 TIME (periods)