Question

What is the principle if a amount is Rs. 25,13,368 for 2 years at 6% per annum, if the interest is compounded 8-monthly?
1. Rs. 32,04,750
2. Rs. 22,34,375
3. Rs. 20,04,370
4. Rs. 22,30,300

Answer 1

Correct Answer - Option 2 : Rs. 22,34,375

Given:

Amount = Rs. 25,13,368

Time = 2 years compounded 8-monthly

Rate = 6%

Formula Used:

For compound interest,

Amount = P(1 + R/100)n

where,

P = principle.

R = rate

n = number of years

Calculation:

Time 2 years

⇒ Time = 2 × 12

⇒ TIme = 24 months

Compounded 8 monthly,

⇒ Time = 24/8

⇒ Time = 3

Rate = 6% per year,

When compounded 8-monthly,

⇒ Rate = 6 × 8/12

⇒ Rate = 4%

Amount = P(1 + R/100)n

⇒ 25,13,368 = P(1 + 4/100)³

⇒ 25,13,368 = P(1 + 1/25)³

⇒ 25,13,368 = P(26/25)³

⇒ 25,13,368 = P × 26/25 × 26/25 × 26/25

⇒ P = (25,13,368 × 25 × 25 × 25)/(26 × 26 × 26)  

⇒ P = 143 × 25 × 25 × 25 

⇒ P = Rs. 22,34,375

∴ Principle is Rs. 22,34,375.