Question

The difference between the compound interest and simple interest for 2 years on a sum of money is rs. 60. If the simple interest for 2 years be rs. 1440, the rate percent is:-

Answer 1

Answer:

The rate of interest is 8.33%

Step-by-step explanation:

Let the rate of interet is r% and amount be Rs. P

If the principle amount is P, rate r% and number of years n then the simple interest is given by

$\boxed{I=\frac{Prn}{100}}$

And the interest after two years if compound interest is applicable, is given by

$\boxed{I=P-P(1+\frac{r}{100})^n}$

Thus

Simple interest after 2 years = 1440

$\implies \frac{P\times r\times2}{100}=1440$

$\implies P\times r=1440\times 100/2$

$\implies P\times r=72000$

The comound interest will be

$I=P-P(1+\frac{r}{100})^2$

According to the question

$P-P(1+\frac{r}{100})^2-1440=60$

$\implies P[1-(1+\frac{r}{100})^2]=60+1440$

$\implies \frac{72000}{r} [1-1+\frac{2r}{100}+\frac{r^2}{10^4} ]=1500$

$\implies \frac{72000}{r} [\frac{200r+r^2}{10000}]=1500$

$\implies \frac{72r}{r} [\frac{200+r}{10}]=1500$

$\implies 200+r=1500\times\frac{10}{72}$

$\implies 200+r=208.33$

$\implies r=208.33-200=8.33$

Therefore, the rate of interest is 8.33%