The difference between the simple interest and compound interest on a certain sum of money for 2 years at 20% interest per annum is ₹964. What is the sum (in ₹)?

Correct option is A

Given:​

Rate of interest = 20%

Time = 2 years

Difference between CI and SI = ₹964

Formula Used:

​$$Amount = Principle \times \left(1+ \frac{r}{100}\right)^{t}$$​​

​$$SI = \frac{P\times R\times T}{100}$$ 

Solution:

​$$CI= Principle \times (1+ \frac{r}{100})^{t} - P$$​​

Difference = CI -SI for two years

​$$964= \left[P \times \left(1+ \frac{20}{100}\right)^{2} -P\right] - \frac{P\times 20\times 2}{100}$$​​

​$$964=P \left[ 1+ \frac{1}{5}\right]^{2}-1 - \frac{ 40}{100}$$​​

​$$964=P \left( \frac{36}{25}-1 - \frac{ 2}{5}\right)$$​​

​$$964 = P \left( \frac{ 36-10-25}{25}\right)$$​​

​$$964 = P \left(\frac{ 1}{25}\right)$$​​

​$$P = 964\times 25$$​​

​$$P = ₹24,100$$ 

Thus, Principle is ₹24,100

Alternative Method:

For 1^st year the SI and CI will be same.

For 2^nd year the interest on interest accumulated in 1^st year will be the difference between the SI and CI

Hence 20% of that interest is ₹964

So 100% = ₹4820

So ₹4820 is the interest accumulated in 1^st year and is same for both SI and CI

So 20% of amount is ₹4820

So 100% =$$4820 \times \frac{100 }{20}$$​= ₹24,100