Question

You need a 35-year, fixed-rate mortgage to buy a new home for $340,000. Your mortgage bank will lend you the money at an APR of 6.35 percent for this 420-month loan. However, you can afford monthly payments of only $1,800, 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 $1,800? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Balloon payment $

Answer 1

Answer: $338712.36

Step-by-step explanation:

Given the following :

APR = 6.35% = 0.0635

Monthly payment = $1800

Cost of home = $340,000

Period (t) = 420

Monthly rate = 0.0635 / 12

Amount paid on loan = PV of monthly payment :

PMT(1 - (1 / (1 + r)^t)) / r

1800[(1 - (1 / (1 + 0.0635/12)^420)) / r]

1800[ (1 - (1 /9.1764488)) / r

1800[ 1 - 0.1089746] / (0.0635 / 12)

1800 [168.38275]

= $303088.95

Hence, amount yet to pay :

$340,000 - $303088.95 = $36911.05

Hence, balloon payment :

36911.05( 1 + r)^t

36911.05(1 + 0.0635/12)^420

36911.05(1 + 0.0052916)^420

36911.05(1.0052916)^420

36911.05 × 9.1764488

= $338712.36