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Question

Rakesh borrowed ₹60,000 at 12% per annum compound interest. If he pays 50% of the sum borrowed at the end of the first year and 50% of the remaining loan at the end of the second year, then find the amount of loan outstanding at the beginning of the third year.

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Solution

Given, P = ₹60,000 and R = 12

For the first year:

I = PTR100

= 60,000×1×12100

= ₹7,200

Given that he pays off 50% of the amount borrowed.
Hence amount paid back by him
= 50% of 60,000
= ₹30,000

For the second year:

Principal = 30,000 + 7,200

= ₹37,200

I = PTR100

= 37200×1×12100

= ₹4,464

Actual amount due at the beginning of the third year
= 37,200 + 4,464
= ₹41,664

Given that he pays off 50% of the remaining borrowed sum.
50% of 30,000 = ₹15,000

Hence the total amount due at the beginning of the third year
= 41,664 - 15,000
= ₹26,664


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