Assume mortgage rates increase to 7.5 percent and you borrow $329,000 for 30 years to purchase a house. What will your loan balance be at the end of the first 15 years of monthly payments?

Answer:

Total number of periods = 30 * 12 = 360

Monthly rate = 7.5% / 12 = 0.625%

Present value = Monthly payments * [1 - 1 / (1 + r)^n] / r

329,000 = Monthly payments * [1 - 1 / (1 + 0.00625)^360] / 0.00625

329,000 = Monthly payments * [1 - 0.10614] / 0.00625

329,000 = Monthly payments * 143.017627

Monthly payments = $2,300.415733

Remaining periods = 15 * 12 = 180

Present value = Monthly payments * [1 - 1 / (1 + r)^n] / r

Present value = 2,300.415733 * [1 - 1 / (1 + 0.00625)^180] / 0.00625

Present value = 2,300.415733 * [1 - 0.325791] / 0.00625

Present value = 2,300.415733 * 107.873427

Present value = $248,153.73

Loan balance will be $248,153.73