A sum of ₹32,760 was taken as a loan. This is to be paid in three equal annual instalments. If the rate of interest is 20% compounded annually, then the value of each instalment is:

Correct option is C

Given:

Amount taken as loan = ₹32,760

Instalment =3

Rate of interest = 20%

Formula Used:

In case of compound interest

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

Solution:

Let the instalment be x

​$$32760 =\left(\frac{x}{\left(1+\frac{20}{100}\right)}+\frac{x}{\left(1+\frac{20}{100}\right)^{2}}+\frac{x}{\left(1+\frac{20}{100}\right)^{3}}\right)$$​​

​$$32760 =\left(\frac{x}{\left(\frac{120}{100}\right)}+\frac{x}{\left(\frac{120}{100}\right)^{2}}+\frac{x}{\left(\frac{120}{100}\right)^{3}}\right)$$​​

​$$32760 =\left(\frac{5x}{6}+\frac{25x}{36}+\frac{125x}{216}\right)$$​​

​$$32760 =\left(\frac{180x+150x+125x}{216}\right)$$​​

​$$32760 =\left(\frac{455x}{216}\right)$$​​

​$$x= ₹15,552$$​​

Alternative Method:

​$$20\% = \frac{20}{100} =\frac{1}{5}$$​​

5              6 $$\times$$​36

25          36  $$\times$$​ 6

125      216

180        216  

150        216  

125        216

Total

455        216

455 is equivalent to principle and 216 is the instalment 

Now  455 = 32760

​$$216 = \frac{32760}{455} \times 216 = ₹15,552$$​​