Question

Suppose you take out a 30-year mortgage for $197,298 at an annual interest rate of 3.1%. After 16 years, you refinance to an annual rate of 1.3%. How much interest did you pay on this loan?

Answer 1

First we will calculate the value of the mortgage at the end of 16 years as per below:

Here we will use the following formula:

FV = PV * (1 + r%)n

where, FV = Future value, PV = Present value = $197298, r = rate of interest = 3.1%, n= time period = 30

now, putting theses values in the above equation, we get,

FV = $197298 * (1 + 3.1%)16

FV = $197298 * (1 + 0.031)16

FV = $197298 * (1.031)16

FV = $197298 * 1.62981625351

FV = $321559.49

So, the amount at the end of 16 years will be $321559.49

Now, we will calculate the value at the end of 30 years i.e. 14 more years.

Now, the formula is:

FV = PV * (1 + r%)n

where, FV = Future value, PV = Present value = $321559.49, r = rate of interest = 1.3%, n= time period = 30 - 16 = 14

now, putting theses values in the above equation, we get,

FV = $321559.49 * (1 + 1.3%)14

FV = $321559.49 * (1 + 0.013)14

FV = $321559.49 * (1.013)14

FV = $321559.49 * 1.1982080556

FV = $385295.17

So, the amount at the end of 30 years will be $385295.17

Now,

Interest = Amount at the end of 30 years - Initial loan amount

Interest = $385295.17 - $197298 = $187997.17