# How to Solve Interest Rate Problems

by Jackie Lohrey

Interest rate problems use time and the value of money to calculate the cost of borrowing money or the return you can expect on money you invest. Variables in these problems include the amount you start with, the interest rate you receive or pay, an overall time period and, in a compound interest rate problem, a frequency variable that identifies how often interest compounds. Start by identifying and formatting the variables for which you must solve and then “plug” numbers into the correct equation.

## Identification

There are two basic types of interest rate problems. The first is simple interest and the second is compound interest. Simple interest, common in short-term loans and investments, is interest you calculate and add to the starting balance only once. In contrast, compound interest is interest you calculate at various points and add to the principal over the course of the loan or investment.

## Review

Review standard interest rate equations to know what the formulas look like and develop a general idea of how the calculations work. Simple interest follows the format “simple interest = principal * interest rate * time.” Principal is the starting balance, the interest rate is a percentage of the principal a lender is charging or paying you and time is the period between when you take out a loan and repay it in full. Compound interest follows the format “future value = principal * (1+interest rate/compounding periods per year)*(compounding periods * total time).

## Apply Formatting

Format the numbers in interest rate problems correctly. Drop the dollar sign on a principal amount and include two decimal places if the amount includes cents. Format the interest rate as a decimal -- convert a percentage to a decimal format by dividing the interest rate by 100 -- and display time using a whole number if the period involves years and for a period of less than one year, divide the number of days by 365 to get a correct percentage of the year. Format compounding periods -- the number of times interest compounds over the course of one year-- in a compound interest rate problem also as a whole number. As an example, the format for a simple interest rate problem in which the principal is \$1,500.50, the interest rate is 10 percent and the time is 60 days appears as: 1,500.50 * (10/100) * (60/365) The format for a compound interest rate problem in which the principal is \$1,500.50, the interest rate is 10 percent and the time is three years and interest compounds quarterly – or four times each year -- appears as: 1,500.50 * (1+.10/4) * (4*3)

## Solve

Solve interest rate problems by completing the calculations enclosed in parentheses and then solving the calculation by multiplying across the line. After completing this step, the simple and compound interest rate problems in the above examples display as: 1,500.50 *.10 * .16438 = \$24.6652 and 1,500.50 *12.3 = \$1845.62 Solving these interest rate problems tells you the amount of simple interest you will pay or receive at the end of 60 days will be \$24.6652, which you can round to \$24.67, for a total payback amount or return of \$1,525.17. In the compound interest rate problem, the total amount you will repay or will have on hand at the end of three years will be \$1,845.62, consisting of the \$1,500.50 principal amount and \$345.12 in interest.

#### Photo Credits

• Comstock/Comstock/Getty Images