Financial Mathematics
Simple and compound interest
Simple and Compound Interest
Simple interest is calculated only on the original amount (principal). Compound interest is calculated on the principal PLUS accumulated interest. Compound interest grows faster because you earn interest on interest.
Example
Simple Interest
A = P(1 + in)
P = R5 000, i = 8% per year, n = 3 years
A = 5000(1 + 0.08 × 3)
A = 5000(1.24)
A = R6 200
Interest earned = R6 200 − R5 000 = R1 200
Example
Compound Interest
A = P(1 + i)ⁿ
P = R5 000, i = 8% per year, n = 3 years
A = 5000(1.08)³
A = 5000 × 1.259712
A = R6 298.56
Interest earned = R1 298.56 (more than simple interest!)
Note
Remember
Simple: A = P(1 + in) — linear growth. Compound: A = P(1 + i)ⁿ — exponential growth. Always convert the percentage rate to a decimal: 8% = 0.08. Compound interest always gives more than simple interest for n > 1.
Key Vocabulary
PrincipalThe original amount of money invested or borrowed
InterestMoney earned on an investment or charged on a loan
Simple interestInterest calculated only on the principal
Compound interestInterest calculated on principal plus previous interest
RateThe percentage of interest charged per period
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