Finance: Growth & Decay
Simple and compound interest, depreciation
Simple Interest
Simple interest is calculated on the original amount (principal) only. Formula: A = P(1 + in), where A = final amount, P = principal, i = interest rate (as a decimal), and n = number of years.
Example
Simple Interest Example
You invest R5 000 at 8% simple interest for 3 years.
P = 5 000, i = 0.08, n = 3
A = 5 000(1 + 0.08 × 3)
A = 5 000(1 + 0.24)
A = 5 000 × 1.24
A = R6 200
Interest earned = R6 200 − R5 000 = R1 200
Compound Interest
Compound interest is calculated on the principal PLUS any previously earned interest. Formula: A = P(1 + i)^n. This leads to faster growth because you earn 'interest on interest'.
Example
Compound Interest Example
You invest R5 000 at 8% compound interest for 3 years.
A = 5 000(1 + 0.08)^3
A = 5 000(1.08)^3
A = 5 000 × 1.259712
A = R6 298.56
Compare: simple interest gave R6 200, compound gives R6 298.56 — more because of interest on interest!
Note
Remember
Simple interest: A = P(1 + in) — grows in a straight line. Compound interest: A = P(1 + i)^n — grows exponentially. For decay (depreciation), use A = P(1 − i)^n. Always convert percentage to a decimal: 8% = 0.08.
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 original principal
Compound interestInterest calculated on principal plus accumulated interest
DepreciationThe decrease in value of an asset over time
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