Question

A 30-year, $200,000 adjustable-rate mortgage starts out with the rate of 3.6%. The borrower makes only the required payments in the first three years. If after three years the rate resets to 4.5%, what is the new required payment?

Answer 1

Compute the PVIFA at 3.6% and 30 years, using the equation as shown below:

PVIFA = {1 – (1 + Rate)-Number of periods}/ Rate

                   = {1 – (1 + 3.6%)-30}/ 3.6%

            = 18.16376186

Hence, the PVIFA at 3.6% and 30 years is 18.16376186.

Compute the annual payment using the equation as shown below:

Annual payment = Loan amount / PVIFA Rate, Period

                          = Loan amount / PVIFA 3.6%, 30

                          = $200.000/ 18.16376186

                         = $11,010.93493

Hence, the annual payment is $11,010.93493.

After 3 years, the remaining period of the loan would be 27 years.

Compute the PVIFA at 3.6% and 27 years using the equation as shown below:

  PVIFA = {1 – (1 + Rate)-Number of periods}/ Rate

                   = {1 – (1 + 3.6%)-27}/ 3.6%

            = 17.08762029

Hence, the PVIFA at 3.6% and 27 years is 17.08762029.

Compute the unpaid loan balance using the equation as shown below:

Unpaid loan balance = Annual payment * PVIFA Remaining period, Rate

                                = $11,010.93493 * PVIFA 27, 3.6%

                                = $11,010.93493 * 17.08762029

                                =$188,150.6751

Hence, unpaid loan balance after 3 years is $188,150.6751.

Now the interest rate is 4.5%.

Compute the PVIFA at 4.5% and 27 years using the equation as shown below:

  PVIFA = {1 – (1 + Rate)-Number of periods}/ Rate

                   = {1 – (1 + 4.5%)-27}/ 4.5%

            = 15.45130282

Hence, the PVIFA at 4.5% and 27 years is 15.45130282.

Compute the annual payment using the equation as shown below:

Annual payment = Loan amount / PVIFA Rate, Period

                          = Loan amount / PVIFA 4.5%, 27

                          = $188,150.6751/ 15.45130282

                         = $12,177.0104

Hence, the annual payment is $12,177.0104.