A principal of Rs. 3000 amounts to Rs. 3360 in 2 years when compounded at a certain rate of interest. How much will the same principal amount if it was compounded semi-annually?
Solution
Correct Answer: Option E
Formula for CI :
\(A = P\;{\left( {\;1\; + \frac{r}{{100}}\;} \right)^t}\)
Where A is the amount at the end of time t,
P is the Principal,
t is time,
r is rate
Given, a principal of Rs. 3000 amounts to Rs. 3360 in 2 years when compounded at a certain rate of interest.
\(\Rightarrow \;3360\; = \;3000\;{\left( {\;1\; + \frac{r}{{100}}} \right)^2}\)
\(\Rightarrow \;1.12\; = {\left( {1\; + \frac{r}{{100}}} \right)^2}\)
\(\Rightarrow \;1.058\; = \;1\; + \frac{r}{{100}}\)
⇒ r = 5.8 %
If it was compounded semi annually
\(A\; = \;P\;{\left( {\;1\; + \frac{r}{{2\; \times \;100}}\;} \right)^{t\; \times \;2}}\)
\(A\; = \;3000{\left( {\;1\; + \;\frac{{5.8}}{{100\; \times \;2\;}}} \right)^{\left( {2\; \times \;2} \right)}}\;\;\)
⇒ A = 3000 (1 + 0.029)4
⇒ A = 3000 × 1.1211
⇒ A = 3363.43
∵ None of the options match, hence E is the correct option.
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