Annuities, loans and investments

An annuity is a series of equal payments: saving every month, or paying back a loan. Future value adds up what regular savings grow to; present value tells you how big a loan regular payments can repay.

Key facts

  • Future value: F = x[(1 + i)ⁿ − 1] / i.
  • Present value: P = x[1 − (1 + i)⁻ⁿ] / i.
  • i is the rate per period (yearly rate ÷ 12 for monthly) and n is the number of payments.
  • A sinking fund saves up for something you’ll need to replace.

Worked examples

Example 1

You save R500 at the end of every month for 5 years at 9% a year compounded monthly. How much will you have?

  1. i = 0.09/12 = 0.0075, n = 60.
  2. F = 500[(1.0075)⁶⁰ − 1] / 0.0075
  3. F ≈ 37 712

Answer: R37 712

Example 2

A R200 000 car loan is repaid monthly over 5 years at 12% a year compounded monthly. Find the monthly payment.

  1. i = 0.01, n = 60.
  2. 200000 = x[1 − 1.01⁻⁶⁰] / 0.01
  3. x = 200000 × 0.01 / (1 − 1.01⁻⁶⁰) ≈ 4448.89

Answer: R4 448.89