A sum of Rs.12,300 was taken as a loan. This is to be paid back in two equal annual instalments. If the rate of interest be 5% per annum, compounded annually, find the value of each instalment.

Correct option is C

Given:

Principal (P) = Rs. 12,300
Rate of interest (R) = 5% per annum, compounded annually
Number of instalments (n) = 2 (equal annual instalments)

Formula Used:
Present Value (P) = $$\frac{A}{(1 + R)^1} + \frac{A}{(1 + R)^2}$$​​
Where:
A = value of each instalment
R = rate of interest per annum (in decimal)

Solution:
Let the annual instalment be Rs. A.

​$$12300 = \frac{A}{1.05} + \frac{A}{(1.05)^2} \\ \ \\12300 = A \left( \frac{1}{1.05} + \frac{1}{1.1025} \right) \\ \ \\12300 = A \left( \frac{100}{105} + \frac{10000}{11025} \right)\\ \ \\12300 = A \left( \frac{20}{21} + \frac{400}{441} \right) \\ \ \\12300 = A \times\left(\frac{420+400}{441}\right) \\ \ \\A = \frac{441}{820}\times 12300 = 6615$$​​

Thus, Each instalment = Rs. 6615

Alternate Method: 

5% = + $$\frac{1}{20}$$ 

Thus, Each instalment =Rs. 6615​