Question

When Arpita invests a certain sum of money, she observes that the CI for the second year is ₹ 1380 and for the third year it is ₹ 1587, when it is compounded yearly. Calculate the rate of interest and the sum of money invested.

Answer 1

Given, the CI for the second year is ₹ 1380 and for the third year it is ₹ 1587, when it is compounded yearly.

Compound interest for 1 year = Compound interest after 3 years – Compound interest after 2 years

= ₹ (1587 – 1380)

= ₹ 207

∴ ₹ 207  is the interest on ₹ 1380 for 1 years.

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

∴ `(1380 xx R xx 1)/100 = 207`

⇒ `R = (207 xx 100)/1380`

⇒ R = 15

Amount = `P( 1 + R/100)^T`, where P is the principal, R is the rate of interest and T is the time period

∴ `P(1 + 15/100)^3 - P(1 + 15/100)^2 = 1587`

⇒ `P[(23/20)^3 - (23/20)^2] = 1587`

⇒ `P[12167/8000 - 529/400] = 1587`

⇒ `P[(12167 - 10850)/8000] = 1587`

⇒ `P[1587/8000] = 1587`

⇒ `P = (1587 xx 8000)/1587`

⇒ P = 8000

Hence, the required rate of interest is 15% and the invested sum is ₹ 8000.