You need a 30-year, fixed-rate mortgage to buy a new home for $210,000. Your mortgage bank will lend you the money at a 7.1 percent APR for this 360-month loan. However, you can afford monthly payments of only $950, 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 $950

$573,963

Explanation:

First, calculate the present value of the loan payments using the following formula

PVA = PMT x [ ( 1 + r )^n - 1 ] / [ r ( 1 + r )^n)

PVA = $950 x [ ( 1 + 7.1%/12 )^360 - 1] / [ 7.1%/12 ( 1 + 7.1%/12 )^360)

PVA =  $141,362.32  

Now calculate the difference of Value of loan and the present value of loan payment

Difference = Loan value - PV of loan payment = $210,000 - $141,362.32 = $68,637.68

This te Ballon payment in present value term, We need to determine the value at the end of the loan term.

Hence we need to calculate the future value of this payment as follow

Future value = Present vale x ( 1 + Monthly Interest rate )^numbers of months

Future value = $68,637.68 x ( 1 + 7.1%/12 )^360

Future value = $573,963.09

Future value = $573,963

Hence the ballon Payment will be $573,963