5.1: Simple Interest
- Page ID
- 139275
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Discussing interest starts with the principal, or amount your account starts with initially. This could be a starting investment, or the starting amount of a loan. Interest, in its most simple form, is calculated as a percent of the principal.
APR – Annual Percentage Rate Interest rates are usually given as an annual percentage rate (APR) – the total interest that will be paid in the year.
For most long term, simple interest loans, it is common for interest to be paid on an annual basis. In that case, interest would be earned each year on the principal.
For example, suppose you borrowed $10,000 from a friend and agree to repay it with 3% annual interest, in 5 years. You would not only repay your friend the $10,000 you borrowed. You would also pay simple interest for each year you had borrowed the money.
|
Year |
Starting balance |
Interest earned |
Ending Balance |
|---|---|---|---|
|
1 |
10,000 |
300.00 |
10300 |
|
2 |
10300 |
300.00 |
10,600 |
|
3 |
10,600 |
300.00 |
10,900 |
|
4 |
10,900 |
300.00 |
11,200 |
|
5 |
11,200 |
300.00 |
11,500 |
The total amount you would repay your friend would be $11,500.00, which is the original principal plus the interest over 5 years.
This process can be generalized with the following formulas:
\[
\begin{array}{l}
I=P_0 r t \\
A=P_0+I=P_0+P_0 r t=P_0(1+r t)
\end{array}
\]
\(I\) is the dollar amount of interest \(A\) is the balance in the account after \(t\) years \(P_0\) is the balance in the account at the beginning (starting amount, or principal). \(r\) is the annual interest rate (APR) in decimal form (Example: \(5 \%=0.05\) ) \(t\) is the number of years we plan to leave the money in the account
Bonds are essentially a loan made to the bond issuer (a company or government) by you, the bond holder. In return for the loan, the issuer agrees to pay interest, often annually. Bonds have a maturity date, at which time the issuer pays back the original bond value.
Bonds are issued with a wide variety of conditions for repayment and interest, often not with simple interest. Be careful to understand the repayment and conditions and interest rules for any bond you consider buying
Suppose your city is building a new park, and issues bonds to raise the money to build it. You obtain a $5,000 bond that pays 4.5% interest annually that matures in 5 years.
Solution
When the bond matures, you would receive back the $5,000 you originally paid, plus $1125 in interest, leaving you with a total of $6125.
Maria invests $16,000 at 3% simple interest for 19 years.
- How much interest will she earn?
- How much is in the account at the end of the 19 year period?
- Answer
-
At the end of the 19 year period, she will have earned $9120 in interest. The balance in her account will be $25120.