©G Dear2008 – Not to be sold/Free to use General Mathematic (HSC) Annuities and Loan Repayments Compound Interest 1 Stage 6 - Year 12 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use

A = P (1 + r)n 8.1 Compound Interest (1/3) An Investment with a single initial contribution. Interest compounds at the end of each period. A = P (1 + r)n A is the future value of the investment. P is the Principal or Money Invested. r is the rate of interest per period as a decimal. n is the number of periods. 2

A = P (1 + r)n 8.1 Compound Interest (2/3) Futurama Episode – Compound Interest Calculate the value of a 93¢ investment at 2¼% for 1000 years, compounding annually. A = P (1 + r)n A = 0.93 (1 + 0.0225)1000 = 0.93 x 1.02251000 ≈ $ 4 300 000 000 3

What is the future value of $10 000 at 10% p.a. for 3 years? 8.1 Compound Interest (3/3) What is the future value of $10 000 at 10% p.a. for 3 years? Principal Year 1 = $10 000 Initial Interest Year 1 = 0.10 x $10 000 = $1 000 Principal Year 2 = $10 000 + $1 000 = $11 000 Interest Year 2 = 0.10 x $11 000 = $1 100 Principal Year 3 = $11 000 + $1 100 = $12 100 Interest Year 3 = 0.10 x $12 100 = $1 210 Future Value = $12 100 + $1 210 = $13 310 4