Question

Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount. How much the scooter will cost him.

Answer 1

Cost of the scooter = Rs 22000
Shamshad Ali pays Rs 4000 in cash.
∴ Unpaid amount = Rs 22000 $-$ Rs 4000 = Rs 18000
Number of years taken by Shamshed Ali to pay the whole amount = 18000 $÷$ 1000 = 18
He agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount.

Total amount of instalments:
$$\begin{gathered} 10\%\mathrm{of}\mathrm{Rs}18000+10\%\mathrm{of}\mathrm{Rs}17000+10\%\mathrm{of}\mathrm{Rs}16000.... \\ =1800+1700+1600.... \end{gathered}$$

It is in an A.P. where a = 1800, d = $-$100 and n = 18.
Therefore, total amount of instalments:
$$\begin{gathered} \frac{18}{2}\left[2\times 1800+(18-1)\times -100\right] \\ =9\left[3600-1700\right] \\ =\mathrm{Rs}17100 \end{gathered}$$

∴ Total amount Shamshad Ali has to pay = Rs (22000 + 17100) = Rs 39100