SEQUENCE AND SERIES B3

Harshita 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 10,000 sh at the end of 4 years?

solution

n=4, t=1, R=10%, A₄=10,000, P=?

A_n = P(1 + ^RT/100)ⁿ

A₄ = P(1 + ^(10x1)/100)⁴

A₄ = P(1 + ¹⁰/100)⁴

A₄ = P(¹⁰⁰/100 + ¹⁰/100)⁴

A₄ = P(¹¹⁰/100)⁴  But A₂=10,000,

10,000 = P(1.1)⁴  = P(1.1x1.1x1.1x1.1)  

10,000 = (1.21x1.21)P

10,000 = 1.4641P

10000  =  1.4641P

1.4641      1.4641

10000  =  P

1.4641

P = 6830.13

Hence at the start she invested Tsh 6830.13