Question

The compound interest on a sum of 5,500 at 15% p.a. for 2 years, when the interest is compounded 8 monthly, is:
1. 1.880
2. 1,820.50

3. 11,773.75
4. 11,850​

Answer 1

Answer:

2) is the right Answer of this question

Answer 2

Option(2) is the correct answer.

Given,

Initial amount (P) = Rs. 5500

Rate of interest(r) = 15%

Time(t) = 2 years

Interest is compounded every 8 months (n = 8)

To Find,

The interest = ?
Solution,

Interest is compounded every 8 months = 12/8 per year

Interest is compounded for 2 years = 2(12/8) = 3 times in 2 years

Rate of interest compounded every 8 months = 15*(8/12) = 10%

From the formula of Compound interest,

$A = P(1 + \frac{r}{100} )^t\\A = 5500(1 + \frac{10}{100} )^3\\A = 5500(1 + 0.1 )^3\\A = 5500(1.1 )^3\\A = 5500 * 1.33\\A = 7320.5$

Therefore, the final amount after 2 years will be Rs. 7320.5

Amount of Interest = A - P

Amount of Interest = 7320.5 - 5500

Amount of Interest = Rs. 1820.5

Hence, the compound interest on a sum of 5,500 at 15% p.a. for 2 years, when the interest is compounded 8 monthly, is Rs. 1820.5.