Future value

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.

The process for converting present values to future values is referred to as .

Which of the following is not one of these variables?

The trend between the present and future values of an investment

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

The present value (PV) of the amount deposited

The duration of the deposit (n)

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%, 9%, or 19%.

Identify the interest rate that corresponds with each line.

01234567891020000150001000050000DOLLARS (PV)TIME (periods)ABC

Line A corresponds to , while Line B is consistent with . Line C corresponds to .

Investments and loans base their interest calculations on one of two possible methods: the interest and the 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.

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?

FV=PV(PVrn)FV=PVPVrn

FV=PV+(PVrn)FV=PV+PVrn

FV=PV(PVrn)FV=PVPVrn

FV=PV1rnFV=PV1rn

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

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

FV=(1+r)nPVFV=1+rnPV

FV=PV+(PVrn)FV=PV+PVrn

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

Identify whether the following statements about the simple and compound interest methods are true or false.

	True	False
After the end of the second year and all other factors remaining equal, a future value based on compound interest will never exceed the future value based on simple interest.
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.
All other factors being equal, when interest is paid annually, both the simple interest and the compound interest methods will accrue the same amount of earned interest by the end of the first year.

Dmitri is willing to invest $35,000 for five years, and is an economically rational investor. He has identified three investment alternatives (X, Y, and Z) that vary in their method of calculating interest and in the annual interest rate offered.

Since he can only make one investment during the five-year investment period, complete the following table and indicate whether Dmitri 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?
X	9% compound interest
Y	12% compound interest
Z	12% simple interest