Question

The compound interest on a certain sum at a certain rate percentage p.a. for the second year and third year are Rs. 3,960 and Rs. 4,356 respectively. What sum is the amount of the same sum at the rate in \(2\frac{1}{2}\) years, interest compounded annually?
1. Rs. 43,560
2. Rs. 43,650
3. Rs. 45,837
4. Rs. 45,738

Answer 1

Correct Answer - Option 4 : Rs. 45,738

Given:

The compound interest on a certain sum at a certain rate percentage p.a. for the second year and third year = Rs. 3,960 and Rs. 4,356 respectively.

Formula used:

C. I = P[(1 + R/100)^N – 1]

Where, C. I = compound interest

P = principal

R = rate

N = time

Calculation:

Difference between compound interest for 3rd year = 3960 – 4356 = Rs. 396

Rate of interest = [(396/3960) × 100] = 10%

Let the principal be Rs. P

According to the question:

P[(1 + R/100)N – 1] – P[(1 + R/100) – 1] = 3960

⇒ P[(1 + 10/100)² – 1] – P[(1 + 10/100) – 1] = 3960

⇒ P[(1.1)2 – 1] – [P(0.1)]= 3960

⇒ P = 3960/0.11 = Rs.36,000

Now,

Amount after 2(1/2) years = P × (1 + 10/100)² × [(1 + 10/(2 × 100)]

⇒ [36000 × (121/100) × (21/20)] 

⇒ 18 × 121 × 21 = Rs. 45,738

∴ The compound interest annually is Rs. 45,738.