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 ?

Answer 1

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.