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Question
A man borrows Rs. 10,000 at 5% per annum compound interest. He repays 35% of the sum borrowed at the end of the first year and 42% of the sum borrowed at the end of the second year. How much must he pay at the end of the third year in order to clear the debt ?
Solution
For the first year,
P1 = 10,000, R = 5%
I1 = `(10,000 xx 5 xx 1)/100`
I1 = 500
A1 = 10,000 + 500 = Rs. 10,500.
At the end of the first year, he repays 35% of the sum borrowed so he repays the amount
`= 10,500 - 35%` of 10,000
= 10,500 - `35/100 xx 10,000`
= 10,500 - 3,500
= Rs. 7,000.
For the second year,
P2 = Rs. 7000, R = 5%
I2 = `(7,000 xx 5 xx 1)/100` = 350
A2 = 7000 + 350 = Rs. 7,350
At the end of the second year, he repays 42% of the sum borrowed so he repays the amount =
= 7,350 - `42/100 xx 10,000`
= 7350 - 4200
= Rs. 3150
For the Third year
P3 = Rs. 3150, R = 5%
I3 =`(3150 xx 5 xx 1)/100` = 157.5
A3 = 3150 + 157.5 = Rs. 3307.50
Hence he pays Rs. 3307.50 at the end of the third year in order to clear the debt.
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