Question

A man borrows ₹ 90000 for 2 years at 5% per annum simple interest and immediately invests for 2 years at 5% compounded interest annually. Find his profit.

Answer 1

Given:

• Principal borrowed, (P = ₹ 90,000)
• Time, (T = 2) years
• Rate of interest, (R = 5%) per annum

Step 1: Calculate Simple Interest (SI) on borrowed amount

`SI = (P xx R xx T)/100`

= `(90,000 xx 5 xx 2)/100`

= ₹ 9,000

Amount to repay after 2 years (Simple Interest Amount):

A_SI = P + SI

= 90,000 + 9,000

= ₹ 99,000

Step 2: Calculate Compound Interest (CI) on amount invested 

Compound interest is compounded annually at the same rate and period:

`A_(CI) = P(1 + R/100)^T`

= `90,000 xx (1 + 5/100)^2`

= `90,000 xx (21/20)^2`

Calculate:

`(21/20)^2 = 441/400`

`(21/20)^2 = 1.1025`

A_CI = 90,000 × 1.1025

A_CI = ₹ 99,225

Compound Interest:

CI = A_CI – P

= 99,225 – 90,000

= ₹ 9,225

Step 3: Calculate Profit

Profit = Compound Interest earned – Simple Interest paid

Profit = 9,225 – 9,000

Profit = ₹ 225