Compound Interest Ques 5
Question
The interest received on a sum of money when invested in scheme A is equal to the interest received on the same sum of money when invested for 2 years in scheme B. Scheme A offers simple interest (p.c.p.a.) and scheme B offers compound interest (compounded annually). Both the schemes offer the same rate of interest. If the numerical value of the number of years for which the sum is invested in scheme A is same as the numerical value of the rate of interest offered by the same scheme, what is the rate of interest (p.c.p.a) offered by scheme A ?
(1) 3
(2) $2 \frac{1}{77}$
(3) $3 \frac{4}{99}$
(4) $2 \frac{2}{99}$
(5) 2
(IBPS RRBs Officer Scale-I & II CWE 13.09.2015)
Show Answer
Answer: (4)
Solution: (4)
Let the rate of S.I. be $r \%$ per annum.
$\therefore$ Time $=r$ years
S.I. $=\frac{\text { Principal } \times \text { Time } \times \text { Rate }}{100}$
C.I. = Principal $\left[\left(1+\frac{\text { Rate }}{100}\right)^{\text {Time }}-1\right]$
According to the question,
$\frac{P \times r \times r}{100}=P\left[\left(1+\frac{r}{100}\right)^{2}-1\right]$
$\frac{r^{2}}{100}=1+\frac{r^{2}}{10000}+\frac{2 r}{100}-1$
$\Rightarrow \frac{r}{100}=\frac{r}{10000}+\frac{1}{50}$
$\Rightarrow \frac{r}{100}-\frac{r}{10000}=\frac{1}{50}$
$\Rightarrow \frac{100 r-r}{10000}=\frac{1}{50}$
$\Rightarrow 99 r=\frac{10000}{50}=200$
$\Rightarrow r=\frac{200}{99}=2 \frac{2}{99} \%$ per annum
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