Simple Interest
Theory
Simple interest (also called flat-rate interest) is calculated only on the original principal — the same dollar amount of interest is added every year. The formula \(I = Prn\) needs the rate as a decimal and the time in years. The total owed or held at the end is \(A = P + I\).
Simple interest (also called flat-rate interest) is interest calculated only on the original amount borrowed or invested. The interest amount is the same every year, so the balance grows in a straight line.
The principal (\(P\)) is the amount borrowed or invested at the start. The rate (\(r\)) is the annual interest rate, expressed as a decimal in the formula (\(8.5\%\) becomes \(0.085\)). "p.a." stands for "per annum" — per year.
The time (\(n\)) is always in years. Months must be divided by \(12\); quarters by \(4\); days by \(365\). The total amount at the end is the principal plus the interest: \(A = P + I\).
The simple interest formula:
The total amount at the end (principal plus interest):
Symbols used:
| Symbol | Meaning |
|---|---|
| \(I\) | interest in dollars |
| \(P\) | principal (amount borrowed/invested) |
| \(r\) | annual rate as a decimal |
| \(n\) | time in years |
| \(A\) | total amount at the end |
Monthly repayment on a flat-rate loan over \(n\) years:
How to calculate simple interest
- Convert the rate to a decimal: divide the percentage by \(100\). \(6\%\) becomes \(0.06\).
- Convert the time to years if needed: months \(\div 12\), quarters \(\div 4\), days \(\div 365\).
- Substitute into \(I = Prn\) and multiply.
- If asked for the total, add to get \(A = P + I\). For flat-rate monthly repayments, divide \(A\) by \(12n\).
Rate as decimal: \(0.06\). Time already in years.
| \(I\) | \(=\) | \(P \cdot r \cdot n\) |
| \(I\) | \(=\) | \(8{,}000 \times 0.06 \times 4\) |
| \(I\) | \(=\) | \(\$1{,}920\) |
The interest is \(\textbf{\$1{,}920}\).
Convert \(18\) months to years: \(18 \div 12 = 1.5\) years. Rate \(= 0.072\).
| \(I\) | \(=\) | \(15{,}000 \times 0.072 \times 1.5\) |
| \(I\) | \(=\) | \(\$1{,}620\) |
The interest is \(\textbf{\$1{,}620}\).
Find the interest, then add to the principal.
| \(I\) | \(=\) | \(25{,}000 \times 0.05 \times 6\) |
| \(I\) | \(=\) | \(7{,}500\) |
| \(A\) | \(=\) | \(25{,}000 + 7{,}500\) |
| \(A\) | \(=\) | \(\$32{,}500\) |
Maya will owe \(\textbf{\$32{,}500}\) at the end.
Find total interest, add to principal, divide by number of months.
| \(I\) | \(=\) | \(3{,}600 \times 0.10 \times 2 = 720\) |
| \(A\) | \(=\) | \(3{,}600 + 720 = 4{,}320\) |
| \(\text{months}\) | \(=\) | \(12 \times 2 = 24\) |
| \(\text{payment}\) | \(=\) | \(\dfrac{4{,}320}{24} = \$180\) |
Tom's monthly payment is \(\textbf{\$180}\).
Common pitfalls
Frequently asked questions
What is simple interest?
Simple interest is interest calculated only on the original principal. The same dollar amount is added each year, so the balance grows in a straight line — not exponentially.
What is the simple interest formula?
\(I = P \cdot r \cdot n\), where \(I\) is interest, \(P\) is principal, \(r\) is the annual rate as a decimal, and \(n\) is time in years.
What does p.a. mean?
Per annum — per year. A rate of \(5\%\) p.a. is \(5\%\) per year.
How do you convert months to years for the simple interest formula?
Divide by \(12\). \(18\) months \(= 1.5\) years; \(30\) months \(= 2.5\) years.
What is the difference between simple and flat-rate interest?
They are the same calculation. Flat-rate is the term used for loans, where interest is worked out up front and repayments split equally across months.
How do you find the total amount owed on a simple interest loan?
Calculate \(I = Prn\), then add to the principal: \(A = P + I\).
Video Lesson
- GCSE Maths - How to Calculate Simple Interest (2026/27 exams) Watch
Practice Questions
9 questions available.
Practice Questions