In order to solve compound
interest problems, you should be able to:
There are several types of interest problems. This lesson deals with solving problems where interest is compounded. There are two other types of interest word problems that are dealt with in other word problem lessons: simple interest
and continuously compounded interest
For working with compound
interest problems, we will be using a formula that involves five variables in an exponential equation. Four of the variables will always be given to you in the problem. Your job will be to find the fifth variable. The level of difficulty in solving for that variable
will depend on whether it is located in the exponent
or not. We’ll look at several different types of problems that all use the same formula.
The formula for interest that is compounded is
A represents the amount of money after a certain amount of time
P represents the principle or the amount of money you start with
r represents the interest rate and is always represented as a decimal
t represents the amount of time in years
n is the number of times interest is compounded in one year, for example:
if interest is compounded annually then n = 1
if interest is compounded quarterly then n = 4
if interest is compounded monthly then n = 12
Suppose Karen has $1000 that she invests in an account that pays 3.5% interest compounded quarterly. How much money does Karen have at the end of 5 years?
Let’s look at our formula and see how many values for the variables we are given in the problem.
The $1000 is the amount being invested or P
. The interest rate
is 3.5% which must be changed into a decimal and becomes r = 0.035. The interest is compounded quarterly, or four times per years, which tells us that n = 4. The money will stay in the account for 5 years so t = 5. We have values for four of the variables. We can use this information to solve for A.
So after 5 years, the account is worth $1190.34. Because we are dealing with money in these problems, it makes sense to round to two decimal places. Notice that the formula gives us the total value of the account at the end of the five years. This is not just the interest amount, it is the total amount. Since there are many variables in the equations, there are several ways that problems can be presented. Let’s look at some other examples.