Question

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.​

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.

To Find :- Assuming the interest rate does not change and there are no subsequent deposits, find the account balance on January 1, 2021 ?

Solution :-

from given data we have,

→ P = Rs.250

→ A = Rs.275

→ T = from 1 july 2018 to 1 january 2019 = 6 months = (6/12) = (1/2) year

→ Rate = Let R% per annum .

since for first year CI and SI remains same .

then,

so,

→ A = P - SI

→ A = P - (P * R * T)/100

→ 275 = 250 - (250 * R * 1)/(100 * 2)

→ 275 - 250 = (5R/4)

→ 25 = (5R/4)

→ R = 20%

then, Amount balance on January 1, 2021 ( after two years) will be,

→ A = 275[1 + (20/100)]²

→ A = 275(120/100)²

→ A = 275 * (6/5)²

→ A = 275 * (36/25)

→ A = Rs.396 (Ans.)

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Answer 2

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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