Compound Interest

Year 11

What is Compound interest?

To compound a problem is to add to more trouble on top of the original difficulty

Compound interestr is a similar process through whivch the principle is recalculated each interest period from the previous principle and the interest gained. It is a cumulatibve effect

Compound interest example

Note:

I= Prt 100A = P + I

Year Principle Interest Amount

1 250 25 275

2 275 27.5 302.5

3 302.5 30.25 332.75

4 332.75 33.28 366.03

Compound vs. Simple Interest

For example: P = 250 I = 10% T = 10yrs

Compound vs Simple Interest Return

Question:Is it best for your Bank Interest to be calculated by the month or the year?What does the decision depend upon?

Compound Interest

Amount of interest

Amount of the Interest I = A - PInterest = Principal - Amount

An example

A loan of $1200 is taken out at a compound interest rate of 14.5% per annum. How much is in the account after 3 year? What was earnt

A = P x (1 +r/100)t

A = 1200 x (1+ 14.5/100)3

A = 1200 x 1.501Amount = $1801.35I = A – PI = 1801.35 – 1200 = $601.35

Your turn

Chapter 6 Page 217 Qu1 a, d, f, g, h Qu2 a, c, e Qu3 Qu6 Qu7 a, c, d Qu9

EXT Qu8 Qu10 Qu11

Calculating the interest & time

To find the interest rate per annum, r%, given the values of P, I and t:

r = 100 x IPt

To find the number of years or term of an investment, t years, given the values of P, I and r:

t = 100 x IPr

Example

Find the rate of simple interest if a principal of $6500 increases to $8375 in 5 years.

r = 100 x IPt

I = 8375 – 6500 = 1875r = 100 x 1875 = 5.77%

6500 x 5

Remember A = P + I → I = A - P

To find time you simply use the second equation

Finding the Principal

To find the principal if you have interest amount (I), interest rate (r) and time (t) in years

To find the principal if you have amount (A), interest rate (r) and time (t) in years

Example

If the saving interest rate is 6.25% and Rex wishes to buy a car at $5600 in three years, how much does he need to invest?

P = A / 1 + (It/100) P = 5600/ (1 + (6.25 x 3)/100)P = $4716

Componded Intervals

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Your turn

Ex 6c Page Qu1 Qu2 Qu3 Qu4 Qu5 Qu6 Qu8

Ext Qu10 Qu11 12 Qu13 Qu7

Calculator Activity

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