Question

You need a 30-year, fixed-rate mortgage to buy a new home for $245,000. Your mortgage bank will lend you the money at an APR of 4.8 percent for this 360-month loan. However, you can afford monthly payments of only $900, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at $900

Answer 1

To keep monthly payments at $900 on a 30-year mortgage with an APR of 4.8%, a balloon payment of approximately $149,182.37 would be required.

Step-by-step explanation:

To determine the balloon payment required to keep your monthly payments at $900, we need to calculate the remaining loan balance at the end of the 30-year term. To do this, we can use the formula for the present value of an annuity:

PV = PMT * ((1 - (1 + r)^(-n)) / r)

Where PV is the present value or remaining loan balance, PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.

In this case:

PMT = $900

r = 4.8% / 12 = 0.004

n = 30 years * 12 months = 360 months

Plugging in these values, we get:

PV = $900 * ((1 - (1 + 0.004)^(-360)) / 0.004) ≈ $149,182.37

Therefore, the balloon payment required to keep your monthly payments at $900 would be approximately $149,182.37.