Question

A borrower wishes to take out a 20 year loan of $350,000 with an interest rate of 7.5%. The borrower will make semi-annual payments of X for 20 years, beginning 6 months after the original loan date. In addition, the borrower will pay a single lump sum payment of $25,000 after the 16th payment. Assuming the loan is paid off exactly with the last semi-annual payment of X, calculate X.

Answer 1

1. Present value of 25000 today = $25000 / (1 + Interest per semi annual period)^16

Present value of 25000 today = $25000 / (1.0325)^16

Present value of 25000 today = $14986.46

2. Net Loan Amount = $350000 - 14986.46 = 335013.54

3. Value of X = Net Loan Amount / Present Value annuity factor(3.25%,40)

Value of X = $335013.54 * Interest per semi annual period / [(1 - (1+Interest per semi annual period)^-periods)]

Value of X = $335013.54 * 3.25% / [(1 - (1.0325)^-40)]

Value of X = $335013.54 * 3.25% / [(1 - 0.2782)]

Value of X = $15084.97