3. Future value

The principal 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 into future values is called . This process requires knowledge of the values of three of four time-value-of-money variables. Which of the following is not one of these variables?

The trend between the present and future values of an investment

The present value (PV) of the amount deposited

The duration of the deposit (N)

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

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 21%. Identify the interest rate that corresponds with each line.

012345678910VALUE (Dollars)TIME (Years)PVCAB

Line A:

Line B:

Line C:

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 I, 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:

Compound interest?

FV = PV x (1 + I)NN

FV = (1 + I)NN / PV

FV = PV + (PV x I x N)

Simple interest?

FV = PV x (PV x I x N)

FV = PV + (PV x I x N)

FV = PV - (PV x I x N)

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

Statement	True	False
All other factors being equal, both the simple interest and the compound interest methods will not generate the same amount of earned interest by the end of the first year.
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.
After the end of the second year and all other factors remaining equal, a future value based on compound interest will exceed a future value based on simple interest.

Sarah is willing to invest $35,000 for six 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 six-year investment period, complete the following table and indicate whether Sarah should invest in each of the investments.

Note: When calculating each investments future value, assume that all interest is earned annually. Do not round your intermediate calculations. The final value should be rounded to the nearest whole dollar.

Investment	Interest Rate and Method	Expected Future Value	Make this investment?
L	7% compound interest
M	6% simple interest
P	11% compound interest