Question

The difference between the amount of compound interest and simple interest accured on an amount of Rs. $26000$ at the end of $3$ years is Rs. $2994.134$. What is the rate of interest ?

• A. $22\%$
• B. $17\%$
• C. $19\%$
• D. $24\%$

Answer 1

Answer: (C)

$19\%$

Given,

$P=Rs.26000$

Time $=3$ years

Let rate $=R\%$

Difference in CI and SI $=2994.134$

Difference in CI and SI for $3$ years is given by formula,

$=P\times {\frac{R}{100}}^2\times \left[\right(\frac{r}{100})+3]$

$2994.134\times 100\times 100=26000\times R^2\times \left[\right(\frac{r}{100})+3]$

or, $1151.59=\frac{R^3}{100}+3R^2$

or, $R^3+300R^2=1151.59\times 100$

[ At this point we choose hit and trial method and by that we get that if we keep $R=19$, we get

or, ${19}^3+300\times {19}^2=115159$

or, $6859+300\times 361=115159$

or, $6859+108300=115159$

or $115159=115159$

That is RHS = LHS, thus $19\%$ is required rate.