A sum is borrowed for two years at the rate of 5% compound interest per annum, compounded annually. If it is paid back in two equal annual instalments of ₹882, then the sum borrowed is:

Correct option is C

Given:

Rate of interest = 5%

Equal installment = ₹882

Time = 2 years

Formula Used:

In case of compound interest

Borrowed money = $$\frac{x}{(1+\frac{r}{100})}+\frac{x}{(1+\frac{r}{100})^{2}}+\frac{x}{(1+\frac{r}{100})^{3}} .…$$​​

Where x is the installment

Solution:

​$$Borrowed money = \frac{x}{(1+\frac{r}{100})}+\frac{x}{(1+\frac{r}{100})^{2}}$$​​

​$$= \frac{882}{(1+\frac{5}{100})}+\frac{882}{(1+\frac{5}{100})^{2}}$$​​

​$$= \frac{882}{(\frac{21}{20})}+\frac{882}{(\frac{21}{20})^{2}}$$​​

​$$= 882 \times \frac{20}{21} + 882 \times \frac{400}{441}$$​​

= 840 + 800

= ₹1640