Question

Pankaj takes a loan of Rs. 10000 at $10\%$ per annum compounded annually which is to be repaid in two equal annual instalments: one at the end of the first year and second at the end of the second year. The value of each instalment is:

• A. Rs. 5760
• B. Rs. 5500
• C. Rs. 5650
• D. Rs. 5800

Answer 1

The correct option is A Rs. 5760

Let the value of each installment is X, Total amount is P

$P=X(K+K^2+K^3+...................),WhereK=\frac{100}{100+r}$ Here only two years and r is $10\%$ then

$P=X(K+K^2)$

$10000=x\{\frac{10}{11}+{\left(\frac{10}{11}\right)}^2\}$

X = 5761.9

Alternatively

$10,000(1.1{)}^2=x[1+\left(1.1\right)]$

x = 5761.9