Consumer Mathematics: Financial Management
How to Work out compound interest
Use this to find the value of savings that earn interest which is added back over several periods.
Before you start
- Changing a percentage to a decimal
- Using the power key on a calculator
- Order of operations: brackets, then powers
- Substituting numbers into a formula
When to use it
Use this to find the value of savings that earn interest which is added back over several periods.
The steps
- Identify the principal (P), the rate (r), how often interest is added (n) and the time (t).
- Use the given maturity-value formula MV = P(1 + r/n)nt.
- Put the rate in as a decimal, not a percentage.
- Work out the bracket first, then raise it to the power.
- Multiply by the principal to get the final value.
Worked example
RM2000 is saved at 6% per year, compounded once a year. Find the maturity value after 3 years.
- Identify the values: P = RM2000, r = 6% per year, n = 1 (once a year), t = 3 years.
- Use the formula MV = P(1 + r/n)nt.
- Put the rate in as a decimal: r = 0.06.
- Work out the bracket first: 1 + 0.06/1 = 1.06; then raise it to the power nt = 3: 1.06³ = 1.191016.
- Multiply by the principal: 2000 × 1.191016 = 2382.032.
A second example, with a twist
Here interest is compounded quarterly, so n = 4: the rate becomes r/n = 0.02 and the power becomes nt = 8. RM5000 is saved at 8% per year, compounded quarterly.
Find the maturity value after 2 years.
- Identify the values: P = RM5000, r = 8% per year, n = 4 (quarterly), t = 2 years.
- Use the formula MV = P(1 + r/n)nt.
- Put the rate in as a decimal: r = 0.08, so r/n = 0.08/4 = 0.02.
- Work out the bracket first: 1 + 0.02 = 1.02; then raise it to the power nt = 4×2 = 8: 1.02⁸ = 1.171659.
- Multiply by the principal: 5000 × 1.171659 = 5858.30.
Formulae you may need
Formula pages
- Law of indices (product)
- Law of indices (quotient)
- Law of indices (power)
- Fractional index
- Maturity value (compound)
- Total repayment
Practise this in a KBAT problem
Frequently asked questions
Why do I use r/n and nt instead of just r and t?
Because interest is added n times a year, not once. Each period earns a smaller rate r/n, and over t years there are nt of these periods.
When n = 1 the formula becomes the simple yearly version P(1 + r)t.
Should I round in the middle of the working?
No. Keep as many decimal places as you can while working out the power, and only round the final answer to two decimal places (the nearest sen).
Rounding early makes the last few ringgit wrong.
What is the difference between simple and compound interest?
Simple interest is worked out on the original principal every period, so it is the same each time. Compound interest adds the interest back into the balance, so later periods earn interest on interest and the total grows faster.