Question

(a) At a certain rate of compound interest, Rs 250 deposited on July 1, 2018 has to accumulate to Rs 275
on January 1, 2019. Assuming the interest rate does not change and there are no subsequent deposits,
find the account balance on January 1, 2021. [03]
(b) You take Rs 500 out of your weekly pay check (you get paid at the end of every week) and deposits in
a fund paying interest 5.2% compounded weekly. You do this for 96 weeks and then stops. How much
in your fund at the end of two years?

Answer 1

Given  : At a certain rate of compound interest, Rs 250 deposited on July 1, 2018 has to accumulate to Rs 275 on January 1, 2019.

Assuming the interest rate does not change and there are no subsequent deposits,

To find :  the account balance on January 1, 2021.​

Solution:

One more assumption : Compound interest R % per annum

and compounding is done on 1st January

Balance as on July 1, 2018  = 2018

Rs 275 on January 1, 2019

Hence time period = 6 months = 1/2 years

for this 6 months SI will be applicable as its less than compounding period.

interest = 275 - 250 = Rs 25

SI = P * R * T /100

=> 25  = 250 * R * (1/2)/100

=> R = 20%

A = P (1  + R/100)ⁿ

on 1st Jan 2019 = 275  hence till 1 Jan 2021 = 2 Years

A = P( 1 + R/100)ⁿ

P = 275 , R = 20 % , n = 2 years

=> A = 275 ( 1 + 20/100)²  = 396   Rs

the account balance on January 1, 2021.​ = Rs 396

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