Question

Ranjan invests ₹ 15,360 for 2 years at a certain rate compounded annually. At the end of one year, it amounts to ₹ 16,320. Calculate

1. the rate of interest
2. the amount at the end of second year.

Answer 1

Given:

• Principal (P) = ₹ 15,360
•  Amount at the end of the first year (A1) = ₹ 16,320
•  Time (n) = 1 year for the first year, and 2 years in total.

i. Rate of interest (R):

We can use the compound interest formula for the first year to find the rate of interest:

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

For the first year:

`A_1 = P(1 + R/100)`

Substituting the known values:

`16,320 = 15,360(1 + R/100)`

Now solve for R:

`(16,320)/(15,360) = 1 + R/100`

⇒ `1.06 = 1 + R/100`

⇒ `R/100 = 0.06`

⇒ R = 6%

So, the rate of interest is 6%.

ii. Amount at the end of the second year:

Now, we calculate the amount at the end of the second year using the formula:

`A = P(1 + R/100)^2`

Substituting the known values:

`A = 15,360(1 + 6/100)^2`

= 15,360 × 1.06²

= 15,360 × 1.1236

A = ₹ 17,340

So, the amount at the end of the second year is ₹ 17,340.