Question

Aparna borrows a sum of ₹ 2500 for 2 years 3 months at 8% p.a. compounded annually. Find

1. the CI for 2 years 
2. the amount at the end of 2 years 3 months.

Answer 1

The problem involves calculating compound interest (CI) and the amount for a principal sum borrowed at a given rate of interest compounded annually. The time period is given as 2 years and 3 months. Since the interest is compounded annually, the interest is compounded once every year.

For the first part, we calculate the compound interest for 2 years. For the second part, since the interest is compounded annually, the extra 3 months will not complete another full year, so we calculate the simple interest for the remaining 3 months and add it to the amount after 2 years.

Identify the given values:

Principal (P) = ₹ 2500 

Rate of interest (R) = 8% per annum

Time (T) = 2 years 3 months = 2.25 years

Calculate the amount after 2 years (compounded annually)

Formula for compound amount:

`A = P xx (1 + R/100)^n`

where n is the number of years.

For 2 years:

`A_2 = 2500 xx (1 + 8/100)^2`

= `2500 xx (1.08)^2`

Calculate:

(1.08)² = 1.1664

So, A₂ = 2500 × 1.1664

= 2916

i. Calculate the compound interest for 2 years:

Compound Interest (CI) = Amount – Principal

CI₂ = 2916 – 2500

= 416

Calculate the amount for the remaining 3 months:

Since interest is compounded annually, for the extra 3 months which is `1/4` of a year, we calculate simple interest on the amount after 2 years.

Simple Interest (SI) for 3 months:

`SI = P xx R/100 xx T`

Here,

Principal = Amount after 2 years = ₹ 2916

Rate = 8%

Time = 3 months = 0.25 years

Calculate:

`SI = 2916 xx 8/100 xx 0.25`

= 2916 × 0.08 × 0.25

= 2916 × 0.02

= 58.32

ii. Calculate the total amount at the end of 2 years 3 months:

A = Amount after 2 years + SI for 3 months

= 2916 + 58.32

= 2974.32