# What is the difference between the compound interests on Rs. 5000 for $$1\frac{1}{2}$$ years at 4% per annum compounded yearly and half-yearly?

A. Rs. 2.04

B. Rs. 3.06

C. Rs. 4.80

D. Rs. 8.30

**Answer: Option A **

__Solution(By Examveda Team)__

$$\eqalign{
& {\text{C}}{\text{.I}}{\text{.}}\,{\text{when}}\,{\text{interest}}\,{\text{compounded}}\,{\text{yearly}} \cr
& = Rs.\left[ {5000 \times \left( {1 + \frac{4}{{100}}} \right) \times \left( {1 + \frac{{\frac{1}{2} \times 4}}{{100}}} \right)} \right] \cr
& = Rs.\left( {5000 \times \frac{{26}}{{25}} \times \frac{{51}}{{50}}} \right) \cr
& = Rs.5304 \cr
& {\text{C}}{\text{.I}}{\text{.}}\,{\text{when}}\,{\text{interest}}\,{\text{in}}\,{\text{compounded}}\,{\text{half - yearly}} \cr
& = Rs.\,\left[ {5000 \times {{\left( {1 + \frac{2}{{100}}} \right)}^3}} \right] \cr
& = Rs.\,\left( {5000 \times \frac{{51}}{{50}} \times \frac{{51}}{{50}} \times \frac{{51}}{{50}}} \right) \cr
& = Rs.\,5306.04 \cr
& \therefore {\text{Difference}} = Rs.\,\left( {5306.04 - 5304} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,2.04 \cr} $$
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in yearly(1.5 yr or 1yr+1/2yr)

5000+5000*4%+5200*4%*0.5=5304

in half yearly

5000+5000*2%+5100*2%+5202*2%=5306.04

so difference

5306.04-5305=2.04