Compound Interest Calculator (CAPS Financial Maths)

Free compound interest calculator using the CAPS formula A = P(1 + i)ⁿ. Choose the compounding period and see the accumulated amount and total interest in rands.

Enter the principal, the nominal annual interest rate, the number of years and the compounding period to get the accumulated amount using the CAPS formula A = P(1 + i)ⁿ. It does the same calculation as the compound-interest questions in Paper 1, so it is a quick way to check an answer you have worked out by hand. In the exam you must still show i, n, the substitution and the final amount rounded to the nearest cent.

How it works

  • The nominal annual rate is divided by the number of compounding periods per year to get i.
  • The number of years is multiplied by the same number of periods to get n.
  • The accumulated amount is A = P(1 + i)ⁿ, and total interest is A − P.
  • Changing the compounding period changes both i and n; the nominal annual rate stays the same.
  • Worked example: R5 000 at 8% p.a. compounded monthly for 5 years gives i = 0.08/12 and n = 60, so A = 5 000(1 + 0.08/12)⁶⁰ ≈ R7 449.23, and the interest earned is about R2 449.23.

Frequently asked questions

Is this simple or compound interest?

Compound. For simple interest use A = P(1 + in), which grows in a straight line rather than a curve.

Why does monthly compounding give more than annual?

Interest is added more often, so later interest is calculated on a larger balance.

How do I find the effective annual rate?

Use 1 + i_eff = (1 + i_nom/m)ᵐ, where m is the number of compounding periods per year. For example, 12% p.a. compounded monthly is an effective rate of about 12.68% p.a.

Does it work for depreciation?

No. Reducing-balance depreciation uses A = P(1 − i)ⁿ, where the value falls each period, and straight-line depreciation uses A = P(1 − in).

Can I use it for annuities?

No. Regular payments, such as a monthly savings plan or a loan, need the future value or present value annuity formulas, which are on the information sheet.

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