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A bank offers the personal loan at simple interest, rate of interest for 1st 2 years is 6%, for the next 4 years it is 8% and for the period beyond 6 years it is 10% per annum. If a person took a personal loan of Rs. 20L and paid Rs. 32.8L after some years. Find the number of years after which he repaid the loan.

A bank offers the personal loan at simple interest, rate of interest for 1st 2 years is 6%, for the next 4 years it is 8% and for the period beyond 6 years it is 10% per annum. If a person took a personal loan of Rs. 20L and paid Rs. 32.8L after some years. Find the number of years after which he repaid the loan. Correct Answer 8 years

Let the person repaid the loan after x years

Cumulative Rate of simple interest for x years (R) = (2 × 6 + 4 × 8 + (x – 6) × 10) = (10x – 16)%

⇒ Simple interest for x years on 20L = (2000000 × R) /100 = 20000R = 20000 × (10x – 16)

Since total amount of money paid by him to the bank at the end of x years = Rs. 3280000

⇒ Interest = 320000 - 2000000 = Rs. 1280000

⇒ 20000 × (10x – 16) = 1280000

⇒ (10x – 16) = 64

⇒ 10x = 80

⇒ x = 8

∴ The person repaid the loan after 8 years.

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