SEQUENCE AND SERIES B2

Caroline invested a certain amount of money in a bank which gives an interest rate of 20% compounded annually. How much did she invest at the start if she got 6,000 sh at the end of 3 years?

Solution

n=3, t=1, R=20%, A₃=6,000, P=?

A_n = P(1 + ^RT/100)ⁿ

A₃ = P(1 + ^(20x1)/100)³

A₃= P(1 + ²⁰/100)³

A₃ = P(¹⁰⁰/100 + ²⁰/100)³

A₃ = P(¹²⁰/100)³  But A₃=6,000,

6,000 = P(1.2)³  = P(1.2x1.2x1.2)  

6,000 = 1.728P

6000  =  1.728P

1.728      1.728

6000  =  P

1.728

P = 3472.22

Hence at the start she invested Tsh 3472.22