SEQUENCE AND SERIES A14

Salma invested a certain amount of money in a bank which gives an interest rate of 10% compounded annually. How much did she invest at the start if she got 8000 sh at the end of 2 years?

solution

n=2, T=1, R=10%, A₂=8000, P=?

A_n = P(1 + ^RT/100)ⁿ

A₂ = P(1 + ^(10x1)/100)²

A₂ = P(1 + ¹⁰/100)²

A₂ = P(¹⁰⁰/100 + ¹⁰/100)²

A₂ = P(¹¹⁰/100)²  But A₂=8000,

8000 = P(1.1)²  

8000 = 1.21P

8000  =  1.21P

1.21       1.21

8000  =  P

1.21       

P = 6611.57

Hence at the start she invested Tsh 6611.67