A sum of ₹8,000 invested at 10% p.a. amounts to ₹9,261 in a certain time, interest compounded half-yearly. What will be the compound interest (in ₹) on the same sum for the same time at double the earlier rate of interest, when interest is compounded annually?
Answer & explanation
Correct answer: option 3
Interest is compounded half - yearly,
Rate of interest = \(\frac{10}{2}\)% = 5%
The Formula that we used here is -
Amount = P$(1 \;+\; \frac{R}{100})^t$
Compound Interest = Amount - Principal
9261 = 8000 [ 1 + \(\frac{5}{100}\)]t
\(\frac{9261}{8000}\) = [ \(\frac{21}{20}\)]t
(\(\frac{21}{20}\))³ = [ \(\frac{21}{20}\)]t
So, t = 3
Hence time = 1 year 6 months
Double the rate = 20%
Amount = P$(1 \;+\; \frac{R}{100})^t$
= 8000 [ 1 + \(\frac{20}{100}\) ] × [ 1 + \(\frac{10}{100}\) ]
= 8000 [ \(\frac{6}{5}\) ] × [ \(\frac{11}{10}\) ]
= 10560
So, Compound interest is = 10560 - 8000
= Rs. 2560