Question

A certain sum amounts to ₹ 17,640 in 2 years and to ₹ 18,522 in 3 years at compound interest. Find the rate and the sum.

Answer 1

Given:

• Amount after 2 years = ₹ 17,640 
• Amount after 3 years = ₹ 18,522 
• We need to find:
  • The rate of interest (R) 
  • The principal (P)

Step 1: Use the information about the two amounts

Let the principal be P and the rate of interest be R%.

From the compound interest formula:

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

We know that:

• After 2 years, the amount is ₹ 17,640, so:
  `17,640 = P(1 + R/100)^2`

• After 3 years, the amount is ₹ 18,522, so:
  `18,522 = P(1 + R/100)^3`

Step 2: Find the ratio of the two amounts

To eliminate P, divide the second equation by the first:

`(18,522)/(17,640) = (P(1 + R/100)^3)/(P(1 + R/100)^2)`

⇒ `(18,522)/(17,640) = (1 + R/100)`

⇒ `1.05 = (1 + R/100)`

⇒ `R/100 = 0.05`

⇒ R = 5%

Step 3: Find the principal

Now that we know the rate is 5%, substitute R = 5 into the first equation to find P:

`17,640 = P(1 + 5/100)^2`

⇒ `17,640 = P xx (1.05)^2`

⇒ `17,640 = P xx 1.1025`

⇒ `P = (17,640)/(1.1025)`

⇒ P = 16,000