If the difference between the simple interest and compound interest earned on an amount at 15 p.c.p.a. at the end of 3 years is Rs. 595.35, what is the principal sum?
Solution
Correct Answer: Option A
Let the principal sum be Rs. x
We know the formula for compound interest and simple interest-
\(\Rightarrow {\rm{S}}.{\rm{I}}.{\rm{\;}} = \frac{{P\; \times R\; \times T}}{{100}}\)
\(\Rightarrow {\rm{CI}} = \left[ {{\rm{P}}\left\{ {{{\left( {1 + \frac{{\rm{r}}}{{100}}} \right)}^t} - 1} \right\}} \right]\)
Where,
CI = Compound interest
SI = Simple Interest
P = Principal
R = Rate of interest
T = Time period
Given: Rate of Interest = 15% p.a.
At the end of 3 years, difference between C.I. and S.I = Rs. 595.35
\(\therefore \;\left[ {x\left\{ {{{\left( {1 + \frac{{15}}{{100}}} \right)}^3} - 1} \right\}} \right] - \;\frac{{x\; \times 15\; \times 3}}{{100}}\; = \;Rs.\;595.35\)
\(\Rightarrow \left[ {x\left\{ {{{\left( {\frac{{115}}{{100}}} \right)}^3} - 1} \right\}} \right] - \frac{{45x}}{{100}} = 595.35\)
\(\Rightarrow \left[ {\frac{{4168}}{{8000}}x} \right] - \;\frac{{45x}}{{100}} = \;595.35\)
\(\Rightarrow \;\frac{{567x}}{{8000}} = 595.35\)
⇒ x = Rs. 8,400
Thus, the principal sum =Rs. 8,400.
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