Year 9: Financial mathematics - Compound interest

Compound interest is interest earned not just on the initial amount (principal), but also on the accumulated interest.

The Formula

The formula for calculating compound interest is:

A = P (1 + r/n)^(nt)

Where:

• A = the amount after t years
• P = the principal amount (initial investment)
• r = the annual interest rate (as a decimal)
• n = the number of times interest is compounded per year
• t = the number of years

Examples

Example 1: You invest $1000 at an annual interest rate of 6% compounded annually for 5 years.

A = 1000 (1 + 0.06/1)^(1*5) = 1000 (1.06)^5 = $1338.22

Example 2: You invest $5000 at an annual interest rate of 8% compounded monthly for 3 years.

A = 5000 (1 + 0.08/12)^(12*3) = 5000 (1 + 0.006667)^(36) = $5769.68

Key Points

• Higher interest rates and more frequent compounding lead to greater growth.
• Always express the interest rate as a decimal (e.g., 6% = 0.06).