A had borrowed a certain sum of money and at the end of 2 years, he paid back Rs. 21648.64. The loan was taken for 2 years at a 4% rate of interest compounded semiannually. What was the original sum?
Solution
Correct Answer: Option A
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 = 21648.64, t = 2 years, rate = 4%, compounded semi-annually
If compounded semi-annually ‘r’ becomes ‘r/2’ and ‘t’ becomes 2t.
\(A\; = \;P\;{\left( {\;1\; + \frac{r}{{2\; \times \;100}}} \right)^{t \times 2}}\)
\(\Rightarrow \;21648.64\; = \;P{\left( {\;1\; + \frac{4}{{100\; \times \;2}}} \right)^{2\; \times \;2}}\)
⇒ 21648.64 = P( 1 + 0.02 )4
⇒ 21648.64 = P(1.082432)
⇒ P = 20000
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