A T.V. set is available for ₹19650 cash payment or ₹3100 cash down payment and three equal annual instalments. If the shopkeeper charges interest at the rate of 10% per annum compounded annually, calculate the amount of each instalment. (S.S.C., 2008)
Answer
Answer (as printed):
Explanation
Total cost of the T.V. set = ₹19650. Down payment = ₹3100. Balance = ₹(19650 – 3100) = ₹16550. Let the value of each instalment be ₹x. Then, (P.W. of ₹x due 1 year hence) + (P.W. of ₹x due 2 years hence) + (P.W. of ₹x due 3 years hence) = ₹16550. $\Rightarrow \frac{x}{1+\frac{10}{100}} + \frac{x}{\left(1+\frac{10}{100}\right)^{2}} + \frac{x}{\left(1+\frac{10}{100}\right)^{3}} = 16550$ $\Rightarrow 1210x + 1100x + 1000x = 16550 \times 1331$ $\Rightarrow 3310x = 16550 \times 1331$ $\Rightarrow x = \frac{16550 \times 1331}{3310} = 6655$. Hence, value of each instalment = ₹6655.
Explanation as extracted from the printed page; notation may be imperfect.