A man borrowed a sum of money and agreed to pay off by paying ₹4,200 at the end of the first year and ₹4,410 at the end of the second year. If the rate of compound interest was 5% per annum, find the sum borrowed

Correct option is D

Given:

Rate of interest = 5%

Time = 2 years

Two installments of ₹4200 and ₹4410

Formula Used:

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

Solution:

For installment ₹4410 rate of interest is 5%p.a. and time = 2 years

Let the Principle be P

$$4410= P \times (1+ \frac{5}{100})^{2}$$​

​$$4410 = P \times (\frac{441}{400})$$​​

​$$P = 4410 \times (\frac{400}{441})$$​​

= ₹4000

For installment ₹4200 Time = 1 years

Let the Principle be P

​$$4200= P \times (1+ \frac{5}{100})^{1}$$​​

​$$4200 = P \times (\frac{21}{20})^{1}$$​​

​$$4200 = P \times (\frac{21}{20})^1$$​​

​$$P = 4200 \times (\frac{20}{21})$$​​

= ₹4000

Total sum = 4000 + 4000 = ₹8000