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A man bought a bike by paying a down payment of Rs. 10500 and taking a loan on the remaining amount at 10% p.a. compound interest for two years. If he cleared his loan by paying two equal instalments of Rs. 24200, what is the price of the bike?

A man bought a bike by paying a down payment of Rs. 10500 and taking a loan on the remaining amount at 10% p.a. compound interest for two years. If he cleared his loan by paying two equal instalments of Rs. 24200, what is the price of the bike? Correct Answer Rs. 52500

As we know, a sum of Rs. P borrowed at R% p.a. compound interest for n years can be paid in ‘n’ equal instalments of Rs. ‘x’ such that,

⇒ P = x/{1 + (R/100)n } + x/{1 + (R/100)n – 1} + …… + x/{1 + (R/100)}

Now, let the man took a loan of Rs. ‘P’

⇒ Rate = R = 10%

⇒ Time = n = 2 years

⇒ Instalment = x = Rs. 24200

⇒ P = +

⇒ P = (24200/1.21) + (24200/1.1)

⇒ P = 20000 + 22000

⇒ P = Rs. 42000

⇒ Price of bike = Down payment + Loan = 10500 + 42000 = Rs. 52500

∴ Price of bike is Rs. 52500

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