Question

The compound interest on a sum of ₹15800 for 2 years at 9% per annum, when the interest is compound 8 monthly,is (nearest to a rupee):

• A. ₹2992
• B. ₹3016
• C. ₹3018
• D. ₹2956

Answer 1

Answer:

C. ₹3018

Solution:

Solution :

Given data :

Principal (P) = Rs. 15800

Time = 2 years

Rate = 9% per annum

Rate of Interest is compounded 8 monthly

Concept used :

Interest = Amount – Principal

$Amount = P\times{(1 + \frac{R}{100})}^n$

Calculation :

Rate of Interest is compounded 8 monthly

⇒ Effective rate $(r)= 9\times{\frac{8}{12}}$

⇒ 6%

⇒ No. of cycles $(n) = \frac{(2\times{12})}{8}$

⇒ 3 cycles

$Amount = P\times{(1 + \frac{R}{100})}^n$

⇒ $15800\times{(1 + \frac{6}{100})}^3$

⇒ $15800\times{(\frac{106}{100})^3}$

⇒ $15800\times{\frac{106}{100}}\times{\frac{106}{100}}\times{\frac{106}{100}}$

⇒ $\frac{(79\times{53}\times{53}\times{53})}{(25\times{25})}$

⇒ 18818.05

Interest = Amount – Principal

⇒ 18818.05 – 15800

⇒ 3018.05 ≈ 3018

∴ The compound interest earned is Rs. 3018.