XAT 2019 — QA & DI Question 12

Price of computer = Rs 19,200

Down payment = Rs. 4,800

∴ Amount borrowed (i.e., loan taken) = 19200 – 4800 = Rs. 14,400.

This amount has to be repaid equally over 5 months at 12% p.a. 

Let Rs. x is paid at the end of every month.

Interest charged for 1 month = 12%/12 = 1%

∴ 14400$\left(1+\frac{1\times 5}{100}\right)$ = x$\left(1+\frac{1\times 4}{100}\right)$ + x$\left(1+\frac{1\times 3}{100}\right)$ + x$\left(1+\frac{1\times 2}{100}\right)$ + x$\left(1+\frac{1\times 1}{100}\right)$ + x

⇒ 15120 = 1.04x + 1.03x + 1.02x + 1.01x + x

⇒ 15120 = 5.1x

⇒ x = 15120/5.1 ≈ 2965.

Hence, option (a).