# Three Techniques for Solving Time Value Problems in Finance

by Jacquelyn Jeanty

Financial planning practices work with time value problems in terms of how the value of money changes with time. Time value problems become an issue within a range of different planning scenarios involving profit earnings, loan rates and budgeting practices. Three techniques for solving time value problems involve determining the present, future and recurring values of money over one or more time periods.

### Time Value of Money

Over time, money investments increase in value as a result of interest earning accumulations. Within the lending or loan industry, interest amounts paid represent the cost of borrowing money for a specified period of time. In effect, interest earnings or interest paid determines the time value of a particular investment or debt. As different financial transactions involve varying interest rates and time periods, problems concerning the time value of money attempt to incorporate the effects of time when determining potential profit earnings or debt costs.

### Future Value Technique

Problems concerning the future value of money consider the interest rate applied, the initial investment (or loan) amount and the length of time under consideration. For example, someone placing \$100 in a money market account that earns an annual interest rate of 5 percent can determine the future value of his investment over a 10 year period of time. By multiplying the \$100 by 5 percent, his annual earnings amount to \$5 a year. Multiplied by 10, this \$5 amount equals \$50, so at the end of 10 years, the future value of the initial \$100 investment equals \$150.00. In effect, interest rate amounts ultimately determine the value of a particular money transaction over time.

### Present Value Technique

Present value problems attempt to determine the present or current value of future cash amounts based on time periods and applied interest rates. By working backwards, the present value technique calculates the current value of a future cash earnings amount based on a certain time period and interest rate. In effect, the present value technique “discounts” a future cash amount to arrive at a present value amount. Once calculated, the present value amount equals the amount of money needed to generate the future cash amount. For example, someone looking to generate \$100 in one year using a 10 percent interest rate would need to invest \$90 today. In other words, the future \$100 amount represents the present value of today’s \$90 investment.

### Recurring Value Techniques

Annuity and bond investments involve recurring interest earnings over set periods of time. Some investment products generate annual interest earnings, while others may produce quarterly or biannual earnings. The earnings rate produces a cash flow stream that’s generated by time value effects, or interest rates. Problems involving cash amounts for recurring interest earnings can use present and future value techniques. Since cash flow streams involve multiple amounts -- be it four times a year, annually or biannually -- present or future value techniques add these amounts together when computing a present or future value. For example, the future value of a \$100 annuity investment over 10 years at 10 percent interest equals the sum total of each amount earned per year, or \$200. Present value techniques use the same process in terms of figuring present values for each year’s earnings, which represent future cash amounts.