Question

Principal amount of Rs. 3000 is invested at 10% rate of interest. Interest is added to the principal amount after every 4 years, calculate the time in years when the amount will sum up to Rs. 4500.
1. \(5\frac{2}{7}\) years
2. \(4\frac{5}{7}\) years
3. \(4\frac{2}{7}\) years
4. \(5\frac{5}{7}\) years

Answer 1

Correct Answer - Option 2 : \(4\frac{5}{7}\) years

Given:

P = Rs. 3000

R = 10%

Interest added = after 4 years

Formula used:

I = PRN / 100

Where P = Principal amount, R = Rate of interest in %, N = Number of years, I = Interest earned

A = P + I    

Where A = Amount received

Calculation:

Interest obtained after first 4 years = 3000 × 4 × 10 / 100

⇒ I = Rs. 1200

After 4 years P = 3000 + 1200

⇒ P = 4200

⇒ Remaining amount = 4500 – 4200

⇒ Remaining amount = 300

⇒ Need Rs. 300 more as interest to make the sum Rs. 4500

Let, remaining time be t years

Accordingly,

(4200 × 10 × t)/100 = 300

⇒ t = (300 × 100 / 4200 × 10)

⇒ t = 5 / 7 years

Total time = (4 + (5/7)) years

⇒ Total time = \(4\frac{5}{7}\) years