Question

Suppose you take a $200,000 thirty-year fixed-rate mortgage at 5.25%, two discount points, monthly payments. At the end of the first year you inherit $20,000 from your now-favorite aunt. You decide to apply this $20,000 to the principal balance of your loan.
A. (1 pt) How many monthly payments are remaining after the extra lump sum payment is made?
B. (1 pt) What is your net interest savings over the life of the loan, assuming the loan is held to its maturity?

Answer 1

There is a reduction of 0.25% for one discount point, so for two discount points, the interest rate will decrease by 0.50%. Effective rate = 5.25% - 0.50% = 4.75%

PV (mortgage amount) = 200,000; N (number of payments) = 30*12 = 360; r (monthly rate) = 4.75%/12 = 0.3958%, solve for PMT.

Monthly payment = 1,043.29

A). Principal outstanding after 1 year (or 12 months): PV = 200,000; PMT = -1,043.29; N = 12; rate = 0.3958%, solve for FV.

Principal outstanding = 196,913.85

If 20,000 lump sum payment then principal amount remaining will be 196,913.85 - 20,000 = 176,913.85

If the same monthly payment of 1,043.29 is continued then the number of payments pending will be:

PV = 176,913.85; PMT = -1,043.29; rate = 0.3958%, solve for NPER (NPER function if using excel) or N (if using financial calculator)

Number of monthly payments = 281.58 or 282 payments.

B). Total amount paid if original loan is held for 30 years = 30*12*1,043.29 = 375,586.08

Total interest paid over 30 years = total amount - total principal = 375,586.08 - 200,000 = 175,586.08

Total amount paid if lump sum payment is made after 1 year = (282+12)*1,043.29 = 306,728.63

Total interest paid = 306,728.63 - 200,000 = 106,728.63

Net interest savings = 175,586.08 - 106,728.63 = 68,857.45