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A man took a loan of certain amount from a bank at an interest of 12% p.a. compounded annually for 2 years. If he had taken the same loan on simple interest at the same rate of interest for the same period, he would have to pay Rs. 1296 less to clear his debt. How much money did he borrowed?

A man took a loan of certain amount from a bank at an interest of 12% p.a. compounded annually for 2 years. If he had taken the same loan on simple interest at the same rate of interest for the same period, he would have to pay Rs. 1296 less to clear his debt. How much money did he borrowed? Correct Answer Rs. 90000

Let the sum borrowed be Rs. ‘P’

⇒ Rate = 12% p.a.

⇒ Time = n = 2 years

When the interest is compounded annually,

⇒ CI = Principal ×

⇒ CI on Rs. P = P × = P × = P × (1.2544 – 1) = 0.2544P

In case of simple interest,

⇒ SI = (Principal × Rate × Time)/100

⇒ SI on Rs. P = (P × 12 × 2)/100 = 0.24P

Now, if the man had borrowed the amount on simple interest, he would have to pay Rs. 1296 less as compared to compound interest

⇒ CI = SI + 1296

⇒ 0.2544P = 0.24P + 1296

⇒ 0.2544P – 0.24P = 1296

⇒ 0.0144P = 1296

⇒ P = 1296/0.0144 = Rs. 90000

∴ The man borrowed Rs. 90000

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