You need a 25-year, fixed-rate mortgage to buy a new home for $315,000. Your mortgage bank will lend you the money at an APR of 6.1 percent for this 300-month loan. However, you can afford monthly payments of only $1,550, 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 $1,550?

The answer is $1,441,746.04

Explanation:

Solution

Given that:

The Annual rate = 6.1%

The monthly interests rate = 6.1%/12 = 0.5083%

Monthly payment = $1,550

The time period = $1,441,746.04300 Months

The amount of payment at the end of 300 months is

=1,550 * ((1.005083^300 - 1) / 0.005083

The amount of payment at the end of 300 months is = $1,090,754.66

Thus

Future value of $315,000 = $315,000*1.005083^300

= $1,441,746.04

Now

The balloon payment = $1,441,746.04 - 1,090,754.66

= $350,991.38

Therefore the largeness of this balloon payment will be $1,441,746.04