Simple Compound Interest Simple Interest Interest paid only

Simple & Compound Interest

Simple Interest -Interest paid only on an initial amount deposited or the amount borrowed -The amount is called the PRINCIPLE

Term -The length of TIME in years over which the $$ is deposited or borrowed Often expressed as “PER ANNUM”

Calculating Formula The amount of simple interest accumulated on an investment or loan is calculated using this formula

I = Prt I = the amount of interest earned or due P = the Principle r = the annual interest rate (expressed as a decimal) t = the term of investment or loan

For an investment: Calculate the total value at the end of the term using this formula:

A = P + I A=final value of the investment P=Principle I=Amount of Interest

Example You want to invest $5000 in an account that offers simple interest. How much would the investment be worth at the end of a 2 yr term at 3%?

First change the interest rate to a decimle 3% =. 03 Principle = $5000 Term = 2 yrs

I = Prt I = $5000 x. 03 x 2 ys I= $300 Now calculate the final value A=P+I A= $5000 + $300 A=$5300

Converting Interest to a decimal 4. 75% converted to a decimal =4. 75 ÷ 100 =. 0475

Use the same Principle and calculate at a rate of 3. 75% for 4 yrs I = $5000 x. 0375 x 4 = $750 Calculate the final value A = $5000 + $750 = $5750

Let’s Try Shall we?

Compound Interest

A type of interest that is calculated on the principle, plus any interest PREVIOUSLY earned

Example -If you invest $$ for two years, but earn interest annually… -the second year of interest will be calculated on the initial principle PLUS the interest it earned in the 1 st year

Example -$5000 @ 3% for 2 yrs calculated using COMPOUND Interest Year 1 I = $5000 x. 03 x 1 yr = $150 A = $5000 + $150 = $5150

Example Year 2 I = $5150 x. 03 x 1 = $154. 50 A = $5150 + $154. 50 = $5304. 50 Therefore - $5000 compounded “annually” over 2 yrs @ 3% = a return of $304. 50

Compounding Period If the interest is compounded annually = once/yr Investments can have different compounding periods

Example Interest can be calculated “SEMI-Annually” Twice/year Interest can be calculated “QUARTERLY” 4 x per year

Example Interest can be calculated “MONTHLY” Once/Month Interest can be calculated “DAILY”

Calculation Formula A = P(1+r ) n nt A = Final Value P = Principle r = Interest Rate n = Number of compound periods t = term of investment/loan

Example Calculate the interest earned on $1000 put in an account that offers 4%/annum compounded annually for 2 yrs

Example nt A = P(1+r ) n 1 x 2 A = $1000 x (1 + 0. 04 ) 1 A = $1000 x (1. 04)2 A = $1081. 60

Compare w/Simple Interest I = $1000 x 4% x 2 I = $1000 x. 04% x 2 I = $80 A = $1000 + $80 = $1080 Compound Int. = $1081. 60