A sum of  Rs. 21,000 is borrowed at a rate of 10% p.a. compound interest compounded yearly. It is returned in two equal annual instalments What is the amount of each installment?

Correct option is B

Given:

Principal (P) = Rs. 21,000

Rate of Interest (R) = 10% per annum

Number of Instalments (n) = 2

Formula Used:

P = $$\frac{x}{(1 + \frac{R}{100})} + \frac{x}{(1 + \frac{R}{100})^2} + \dots + \frac{x}{(1 + \frac{R}{100})^n}$$​​

Solution:

Substituting the values:

​$$21,000 = \frac{x}{1.1} + \frac{x}{1.21}$$​​

​$$21,000 = x \left( \frac{1}{1.1} + \frac{1}{1.21} \right)$$​​

​$$21,000 = x \left( \frac{1.1 + 1}{1.21} \right)$$​​

​$$21,000 = x \left( \frac{2.1}{1.21} \right)$$​​

​$$x = 21,000 \times \frac{1.21}{2.1}$$​​

​$$x = \frac{21,000 \times 121}{210 \times 1}$$​​

​$$x = 100 \times 121$$​​

x = Rs. 12,100

Thus, Each instalment is Rs.12,100 

Alternate Solution: 

Rate of interest = 10% = $$\frac{1}{10}$$ 

210 unit  = 21000 

so, 121 unit = $$\frac{21000}{210} \times 121 = ₹12100$$​​