Question

A man borrows Rs. 5,000 at 12 percent compound interest payable every six months. He repays Rs. 1,800 at the end of every six months. Calculate the third payment he has to make at the end of 18 months in order to clear the entire loan.

Answer 1

For 1^st six months :
P = Rs. 5,000, R = 12% and T = 6 months = `1/2` year
∴ Interest = `[ 5,000 xx 12 xx 1]/[ 2 xx 100 ]` = Rs. 300.

And, Amount = Rs. 5,000 + Rs. 300 = Rs. 5,300
Since, money repaid = Rs. 1,800
Balance = Rs. 5,300 - Rs. 1,800 = Rs. 3,500

For 2^nd six months :
P = Rs. 3,500, R = 12% and T = 6 months = `1/2` year

∴ Interest = `[ 3,500 xx 12 xx 1 ]/[ 2 xx 100 ]` = Rs. 210.

And, Amount = Rs. 3,500 + Rs. 210 = Rs. 3,710.
Again money repaid = Rs. 1,800
Balance = Rs. 3,710 - Rs. 1,800 = Rs. 1,910.

For 3^rd six months :
P = Rs. 1,910, R = 12% and T = 6 months = `1/2` year
∴ Interest = `[ 1,910 xx 12 xx 1 ]/[ 2 xx 100 ]` = Rs. 114.60.

And, Amount = Rs. 1,910 + Rs. 114.60 = Rs. 2,024.60
Thus, the 3^rd payment to be made to clear the entire loan is 2,024.60.