Example: A bank issues a $100,000 fixed-rate, 30-year mortgage with a nominal annual rate of 4.5%. If the required rate drops to 4.0% immediately after the mortgage is issued, what is the impact on the value of the mortgage?

Solution: At 4.5%, the required payment is calculated as:

PV = 100,000, I = 4.5/12, N = 360, FV = 0

Compute PMT. PMT = 506.685

In a 4.0% market, the value of the mortgage is:

PMT = 506.685, I = 4.0/12, N = 360, FV = 0

Compute PV. PV = 106,131.

The value of the mortgage has increased by $6,131, or 6.131%.

Q1: A bank issues a $150,000 fixed-rate, 30-year mortgage with a nominal annual rate of 5.5%. If the required rate drops to 5.25% immediately after the mortgage is issued, what is the impact on the value of the mortgage? (Please follow above example to solve this question)