Question

A loan of $10000 is being repaid with level payments at the end of each year for 10years. Assuming 10% effective interstate's per year, the borrower pays an extra x dollars with their 5th payment which allows the same level payments to exactly pay off the loan two years earlier. Find X

Answer 1

The loan repayment is a normal annuity , the present value of which equals loan amount. The level payment (A) is calculated as

A* Present value annuity factor = 10000

=> A * (1-1/1.1^10)/0.1 = 10000

=> 6.14457*A =10000

=> A= $1627.45

Now, the present value of 8 payments of $1627.45 + present value of $X at the end of 5th year should also be equal to loan amount

1627.45/0.1*(1-1/1.1^8)+X/1.1^5 = 10000

=> 8682.35 + X/1.1^5 = 10000

=> X/1.1^5 =1317.653

=> X =2122.09

So, the amount X has to be equal to $2122.09