Question

The amount at compound interest which is calculated yearly on a certain sum of money is ₹ 4840 in 2 years and ₹ 5324 in 3 years. Calculate the rate and the sum.

Answer 1

Given:

• Amount after 2 years = ₹ 4,840 
• Amount after 3 years = ₹ 5,324
• We need to find:
  • The rate of interest (R)
  • The principal (P)

Step 1: Use the compound interest formula

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

We know that the formula for compound interest is:

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

Where:

• A is the amount after n years
• P is the principal
• R is the rate of interest
• n is the time in years

We have:

• After 2 years, the amount is ₹ 4,840:
  `4,840 = P(1 + R/100)^2`
• After 3 years, the amount is ₹ 5,324:
  `5,324 = P(1 + R/100)^3`

Step 2: Find the ratio of the two amounts

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

`(5,324)/(4,840) = (P(1 + R/100)^3)/(P(1 + R/100)^2)`

⇒ `(5,324)/(4,840) = (1 + R/100)`

⇒ `1.1 = (1 + R/100)`

⇒ `R/100 = 0.1`

⇒ R = 10%

Step 3: Find the principal

Now that we know the rate is 10%, substitute R = 10 into the first equation to find P:

`4,840 = P(1 + 10/100)^2`

⇒ `4,840 = P xx (1.1)^2`

⇒ `4,840 = P xx 1.21`

⇒ `P = (4,840)/(1.21)`

⇒ P = 4,000