Ramlal takes a loan of Rs. 10500 at 10% p.a. compounded annually which is to be repaid in to two equal annual installments as one at the end of one year and the other at the end of the second year. The value of each installment is:
Solution
Correct Answer: Option D
Given that rate of interest R = 10%
Annual installment = Rs. X
Total number of installment = 2
Sum borrowed = Rs 10500
Sum borrowed = \(\left( {\frac{X}{{1 + \frac{R}{{100}}}} + \;\frac{X}{{{{\left[ {1 + \frac{R}{{100}}} \right]}^2}}}} \right)\)
\(\Rightarrow 10500 = \left( {\frac{X}{{1 + \frac{{10}}{{100}}}} + \;\frac{X}{{{{\left[ {1 + \frac{{10}}{{100}}} \right]}^2}}}} \right)\)
\(\Rightarrow 10500 = X\;\left[ {\frac{{10}}{{11}} + \;{{\left( {\frac{{10}}{{11}}} \right)}^2}} \right]\)
⇒ x = Rs 6050
Hence, the required amount of one installment is Rs 6050
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