Question

On a certain sum of money, the difference between the CI for a year, payable half-yearly and the SI for a year is ₹ 120. Find the sum lent out, if the rate of interest in both cases is 10% p.a.

Answer 1

Given a certain sum of money, the difference between the CI for a year, payable half-yearly and the SI for a year is ₹ 120.

Rate of interest in both cases is 10% per annum.

Let the given sum be ₹ P.

Simple interest = `(PRT)/100`, where P is the principal, R s the rate of interest and T is the time period

∴ `(P xx 10 xx 1)/100 = P/10`

When the interest is compounded half-yearly, we use the formula, compound interest = `P(1 + R/200)^(2T) - P`, where P is the principal, R is the rate of interest and T is the time period.

∴ Compound interest = `P(1 + 10/200)^2 - P`

= `P(1 + 1/20)^2 - P`

= `P(21/20)^2 - P`

= `(441P)/400 - P`

= `(441P - 400P)/400`

= `(41P)/400`

∴ Compound interest – Simple interest = 120

⇒ `(41P)/400 - P/10 = 120`

⇒ `(41P - 40P)/400 = 120`

⇒ `P = 120 xx 400`

⇒ P = 48000

Hence, the required sum is ₹ 48000.