Question

Assume a $10,000,000 mortgage for an office building. The loan carries a rate of 4.25% based on monthly pay over a 30-year amortization period. The loan has a balloon amount due in 10 years. What is the balloon amount?

Group of answer choices

$7,844,018

$7,901,889

$7,675,923

$,7944,323

Answer 1

Compute the monthly interest rate, using the equation as shown below:

Monthly rate = Annual rate/ 12 months

                      = 4.25%/ 12 months

                      = 0.35416666666%

Hence, the monthly interest rate is 0.35416666666%.

Compute the present value annuity factor (PVIFA), using the equation as shown below:

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

                 = {1 – (1 + 0.0035416666666)-360}/ 0.35416666666%

             = 203.276867386

Hence, the present value annuity factor is 203.276867386.

Compute the monthly loan payment, using the equation as shown below:

Monthly payment = Loan amount/ PVIFA

                             = $10,000,000/ 203.276867386

                             = $49,193.9891075

Hence, the monthly loan payment is $49,193.9891075.

Compute the present value annuity factor (PVIFA), using the equation as shown below:

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

                 = {1 – (1 + 0.0035416666666)-120}/ 0.35416666666%

             = 97.6204685196

Hence, the present value annuity factor is 97.6204685196.

Compute the present value of the monthly payment, using the equation as shown below:

Present value = Monthly payment*PVIFA

                       = $49,193.9891075*97.6204685196

                       = $4,802,340.26502

Hence, the present value of the monthly payment is $4,802,340.26502.

Compute the value of balloon payment, using the equation as shown below:

Balloon payment = (Loan value – Present value of monthly payments)*(1 + Rate)Time

                             = ($10,000,000 - $4,802,340.26502)*(1 + 0.0035416666666)120

                             = $5,197,659.735*1.52844238543

                             = $7,944,323.44401

Hence, the balloon payment is $7,944,323.