1. 20.3 Compound Interest

2. The more common form of interest used is Compound Interest. It is called compound because the interest accumulates each year is added to the principal. Each subsequent year, interest is earned on this total of principal and interest. The interest therefore compounds.

3. The amount of the compound interest varies each year, and therefore there is a non-linear relationship between compound interest and the term of the investment.

4. Whilst simple interest follows a linear relationship because the same amount of interest is added each year, compound interest follows a (non-linear) curve (geometric sequence).

5. Comparing the interest earned from simple interest to that earned from compound interest, we see the advantage to the investor since the amount of compound interest increases over time. Insert graph page 537

6. Compound Interest Formula The amount of money ($A) that would result from investing $P at r% per annum, compounded annually for a period of t years, is: A = P x ( 1 + r ) t 100

7. To calculate the Interest To calculate the Interest I = A – P Or I = P x ( 1 + r ) t – P 100 Using the TI-Nspire CAS, see page 538

8. Total amount owed or invested When compound interest is calculated at a time other than annually, the formula is adjusted to: A = P x ( 1 + r/n ) nt 100 Where $A = the amount of the investment after t years $P = the initial amount r = the interest rate per annum n = the number of times per year interest is compounded t = the number of years

9. Solve for any variable using CAS To use the solve command on your calculator, see page 542. “How to solve for any variable in the compound interest formula using the TI-Nspire CAS.”