Key takeaway: Simple interest is the fee paid for using money, figured only on the starting amount at a fixed yearly rate, so each year adds the same dollar amount.
Grade 77.RP.A.3Ratios, Rates and Percents
Definition of Simple Interest
Simple interest is the fee a bank pays you for keeping money with it, or the fee you pay for borrowing. It is computed only on the starting amount, called the principal, and never on interest already earned.
Because the rate and the principal stay fixed, the same dollar amount of interest is added every year. After 3 years you have collected exactly 3 times the first year’s interest. The final balance is the principal plus all the interest.
Formula and notation
Three factors are multiplied together:
\[I = P \cdot r \cdot t\]
The letter \(P\) stands for the principal (starting amount), \(r\) for the yearly rate written as a decimal, and \(t\) for the number of years. The answer \(I\) is the interest, and the final balance is \(A = P + I\).
Key facts
- The time \(t\) must be in years, so 9 months becomes \(\frac{9}{12} = 0.75\) year.
- Interest grows by the same number of dollars every year, so its graph is a straight line.
- Convert the percent rate to a decimal before multiplying: 4.5% becomes 0.045.
- The principal is the starting amount; interest never gets added into it.
Simple Interest example
Jonas deposits \$1,800 in a savings account that pays 4.5% simple interest per year. How much interest does he earn in 3 years, and what is his balance?
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Identify the values: \(P = 1800\), \(r = 0.045\), \(t = 3\).
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Interest: \(I = 1800 \times 0.045 \times 3 = 81 \times 3 = 243\).
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Balance: \(A = 1800 + 243 = 2043\).
Jonas earns \$243 in interest and ends with \$2,043.
Common mistake
Watch out
Rosa invests \$600 at 5% for 6 months and calculates \(I = 600 \times 0.05 \times 6 = 180\) dollars.
Why it is wrong
The rate is per year, so the time must be in years too. Six months is \(\frac{6}{12} = 0.5\) year, and \(I = 600 \times 0.05 \times 0.5 = 15\) dollars. Putting 6 in for \(t\) overstated the interest twelve times .
Related terms and lessons
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