Formula sheet
Maturity value (compound)
MV = P(1 + r/n)nt is given in the exam, so no memorising is needed. You must know what each letter means, especially that n is the number of times interest is added each year, and remember to work out MV as the final amount, then subtract P if only the interest is wanted.
What the symbols mean
- MV the maturity value, the final amount, in ringgit (RM)
- P the principal, the amount invested, in ringgit (RM)
- r the annual interest rate, written as a decimal (e.g. 4% = 0.04)
- n the number of times interest is compounded per year
- t the time, in years
Given in the exam, or memorise?
MV = P(1 + r/n)nt is given in the exam, so no memorising is needed. You must know what each letter means, especially that n is the number of times interest is added each year, and remember to work out MV as the final amount, then subtract P if only the interest is wanted.
Why it works
Compounding multiplies the balance by the same growth factor every period.
- Each period the rate is r/n, so the balance is multiplied by (1 + r/n).
- In t years there are n × t such periods.
- Multiplying that factor nt times, then by P, gives P(1 + r/n)nt.
Worked example 1
RM5000 is invested at 4% per year, compounded quarterly. Find the maturity value after 2 years.
- List the values: P = 5000, r = 0.04, n = 4 (quarterly), t = 2.
- Substitute into MV = P(1 + r/n)nt: MV = 5000(1 + 0.04/4)4×2.
- Simplify inside the bracket and the exponent: 5000(1 + 0.01)8 = 5000(1.01)8.
- Evaluate (1.01)8 = 1.0828567, then 5000 × 1.0828567 = 5414.28.
Worked example 2
RM8000 is placed in a fixed deposit at 6% per year, compounded annually for 3 years. Find the maturity value.
- List the values: P = 8000, r = 0.06, n = 1 (annually), t = 3.
- Substitute into MV = P(1 + r/n)nt: MV = 8000(1 + 0.06/1)1×3.
- Simplify: 8000(1.06)3.
- Evaluate (1.06)3 = 1.191016, then 8000 × 1.191016 = 9528.13.
Where students go wrong
- Using r as a percentage instead of a decimal, enter 0.04, not 4, inside the bracket.
- Forgetting to divide r by n and to multiply t by n, the exponent is nt, so quarterly for 2 years gives 8 periods, not 2.
- Rounding the (1 + r/n)nt factor too early, or reporting MV as the interest instead of the final amount.
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
What do n and t stand for in the compound formula?
n is how many times interest is added per year and t is the number of years. Compounded quarterly means n = 4; monthly means n = 12.
The exponent nt is the total number of compounding periods over the whole time, which is why interest builds faster than simple interest.
How is compound interest different from simple interest?
Simple interest (I = Prt) is worked out only on the original principal every year. Compound interest adds each period's interest back, so the next period earns interest on interest.
That is why MV = P(1 + r/n)nt grows a little faster than the matching simple-interest amount.
How do I get just the interest, not the maturity value?
MV is the final amount, the principal plus interest together. To get the interest on its own, subtract the principal: interest = MV − P.
For example, if MV = RM5414.28 and P = RM5000, the compound interest earned is RM5414.28 − RM5000 = RM414.28.