Question

Assume that a borrower takes out a $400,000, 30-year mortgage, at a 3.5% annual nominal interest rate. Suppose that the market interest rate for the mortgage above rises to 4.5%. What is the market value of the mortgage, assuming it is the start of month 61?

Answer 1

First let's calculate the yearly payment of mortgage :

PV of the yealy payments is equal to the value of mortgage. Thus, yearly payments are like annuity payments.

We will calculate the yearly payment value through the follwing formula :

PV = $400,000

i = 3.5%

n = 30 years

Putting values in the formula :

$400,000 = C * [(1-(1+3.5%)^-30) / 3.5%)

$40,000 = C* 18.39

C = $21,748.53

After 60 months, that is 5 years, the remainign time of the mortgage would be 25 years.

i = 4.5% (New interest rate)

n = 25 years

C = $21,748.53

Putting these values again in formula to calulate the PV (market) of the mortgage :

PV = $21,748.53 * [(1-(1+4.5%)^-25) / 4.5%]

PV = $21,748.53 * 14.83

PV = $322,491,75

Market value of mortgage a the begining of 61 months due to increase in interest rate to 3.5% would be $322,491,75