Question

You need a 30-year, fixed-rate mortgage to buy a new home for $290,000. Your mortgage bank will lend you the money at a 5.85% APR (semi-annual) for this 360-month loan. However, you can afford monthly payments of only $1,300, 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 $1,300?

Answer 1

We see that the balloon payment is given as

Using Excel=FV((1+5.85%/2)^(2/12)-1,360,1300,-290000)
=383264.27

Using financial calculator

I/Y=(1+5.85%/2)^(2/12)-1

N=360

PMT=1300

PV=-290000

CPT FV=383264.27

Using formula

effective monthly rate=(1+nominal rate/m)^(m/n)-1=(1+5.85%/2)^(2/12)-1=0.4817%

Balloon payment=Loan*(1+effective monthly rate)^number of months-Monthly payment/(effective monthly rate)*((1+effective monthly rate)^number of months-1)=290000*(1+0.4817%)^(360)-1300/(0.4817%)*((1+0.4817%)^360-1)

=383264.27