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

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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 2yr term at 3%?

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

I = Prt I = \$5000 x.03 x 2ys 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 1yr = \$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 2yrs @ 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 A = Final Value P = Principle r = Interest Rate n = Number of compound periods t = term of investment/loan nt

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

Example A = P(1+r ) n A = \$1000 x (1 + 0.04 ) 1 nt 1x2 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

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