Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004

Example from the BrainPop video Year 1Year 2Year 3Year 4 capital $50$53.00$56.18$59.55 interest $3.00$3.18$3.37$3.57 new amount $53.00$56.18$59.55$ % yearly compound interest Section 13C – Compound Interest

6% yearly compound interest capitalinterestnew amount Year 1 $50$3.00$53.00=$50×1.06 Year 2 $53.00$3.18$56.18 =$50×1.06×1.06 =$50×(1.06) 2 Year 3 $56.18$3.37$59.55 =$50×1.06×1.06×1.06 =$50×(1.06) 3 Year 4 $59.55$3.57$63.12 =$50×1.06×1.06×1.06×1.06 =$50×(1.06) 4

6% yearly compound interest capitalinterestnew amount Year 4 $59.55$3.57$63.12 =$50×1.06×1.06×1.06×1.06 =$50×(1.06) 4 Recognize the connection to a geometric sequence: U n + 1 = u 1 r n

Example from the BrainPop Video 6% yearly compound interest Year 4 =$63.12 =$50×1.06×1.06×1.06×1.06 =$50 (1.06) 4 =$50( ) 4 A = C  ( 1 + r/100 ) n

Compound Interest Formulae A = future value C = capital r = interest rate n = # of years A = future value C = capital r = interest rate n = # of years k = # of compoundings in a year A = C  ( 1 + r/100 ) n A = C  ( 1 + r/100k ) nk

From the Formula Booklet

Different Compounding Periods Compounding period yearly1 times per yeark = 1 half-yearly2 times per yeark = 2 quarterly4 times per yeark = 4 monthly12 times per yeark = 12 daily365 times per yeark = 365

From the Subject Guide

To how much will $1000 grow to if it is invested at 12% p.a. for 9 years, compounding annually? Example 1

A bank advertises an annual interest rate of 13.5% p.a. but adds interest to the account monthly, giving a monthly interest rate of 1.125%. Scott deposits $3500 with the bank. How much will he withdraw in 20 months time? Example 2

To what amount will $900 grow to if it is invested at 10% p.a. for 7 years, compounding every 6 months? Example 3

How long will it take $2000 to amount to $4300 if invested at 8% p.a., with interest compounded annually? Use the calculator (find the intersection) Example 4

You want to have $5000 after 2 years. Find the amount you should deposit if the account pays 2.5% annual interest compounded monthly. Example 5

If Iman deposits $5000 in an account that compounds interest quarterly and 2.5 years later the account totals $6000, what rate of interest was paid? Example 6

Section 13D - Depreciation The loss in value over time The r-value is negative A = future value C = capital r = interest rate n = # of years k = # of compoundings in a year A = C  ( 1 + r/100k ) nk

An industrial dishwasher was purchased for ₤2400 and depreciated at 15% each year. a) Find it’s value after six years. b) By how much did it depreciate? Example 7

Use the calculator to determine if it is better to invest $1000 at 9% p.a., compounded semiannually or $1500 at 6.5% simple interest. Example 8

Calculator You may choose to use the Finance application on your calculator. Read Investigation 1 on page 434 for instructions.

Homework 13C.1 #3 13C.2 #3 13C.3 #1,2, 4 13C.5 #1, 5 13C.6 #1, 3 13C.7 #2