Question

The compound interest on a certain sum of money at 6% per annum for 2 years is ₹ 306. Find the simple interest on the same sum for 3 years at 10% per annum.

Answer 1

Step 1: Find the principal sum using the compound interest information.

The formula for compound interest (C.I.) is C.I. = P(1 + r)^t – 1, where P is the principal, r is the annual rate and t is the time in years.

We are given:

• C.I. = 306
• r = 6% = 0.06
• t = 2 years

Substitute the values into the formula:

306 = P(1 + 0.06)² – 1)

306 = P((1.06)² – 1)

306 = P(1.1236 – 1)

306 = P(0.1236)

`P = 306/0.1236`

P = 2475

The principal sum is ₹ 2475.

Step 2: Find the simple interest on the principal sum. 

The formula for simple interest (S.I.) is S.T. = P × r × t.

We will use the principal sum found in the previous step and the new rate and time:

• P = 2475
• r = 10% = 0.10
• t = 3 years

Substitute the values into the formula:

S.I. = 2475 × 0.10 × 3

S.I. = 247.5 × 3

S.I. = 742.5

The simple interest on the same sum for 3 years at 10% per annum is ₹ 742.5.