Question

An amount, at a specific interest rate and when the interest is being compounded yearly, becomes Rs. 4,460 in 3 years and Rs. 6,690 in 6 years. What will be the simple interest of \(4\dfrac{1}{2}\) years at the rate of 10% per annum on the same amount?
1. Rs. 1,285
2. Rs. 1,383
3. Rs. 1,316
4. Rs. 1,338

Answer 1

Correct Answer - Option 4 : Rs. 1,338

Given:

Amount after 3 years with Compound Interest(CI) = Rs. 4460

Amount after 6 years with Compound Interest(CI) = Rs. 6690

Rate of interest(r) for Simple Interest(SI) = 10%

Time(t) for Simple Interest = 4.5 years

Concept used:

The ratio of amount with compound interest for the same rate of interest and same interval of time is equal

Formula used:

SI = (P × r × t)/100

Where P is Principal

Calculation:

Let the principal be Rs. P

The ratio of the amount after 3 years and 6 years is

⇒ 4460/6690 = 2/3

The ratio of principal and amount after 3 years

⇒ P/4460 = 2/3

⇒ P = Rs. 8920/3

SI for 4.5 years is

\(\dfrac{ \frac{8920}{3}\ × \ 10 \ × \ 4.5}{100}\)

⇒ 892 × 1.5 = Rs. 1338.

∴ The simple interest for 4.5 years is Rs. 1338.