Question

You need a 30-year, fixed-rate mortgage to buy a new home for $500,000. You will pay 20 percent down and borrow the rest at an APR of 6 percent compounded monthly. However, you can only make monthly payments of $1,800. The lender offers that you pay off the remaining loan balance at the end of 30 years as a single balloon payment. What will be the amount of the balloon payment if you are to keep your monthly payments at $1,800?

Answer 1

An APR of 6% compounded monthly means, 6/12 = 0.5% per month

As 20% is paid down, amount of loan = 0.80*500,000 = $400,000

Everything is taken in monthly terms

Excel's function =FV can be used to calculate the net future value of the stream of payments of $1800 being made till 30 years and the loan amount of $400,000 taken initially. The result gives the amount of balloon payment required at the end.

=FV(rate.nper,pmt,pv)

here rate is interest rate monthly which is 0.005, nper is the number of periods which is 30*12 = 360, pmt is the regularperiodic payments which is $1800 and pv is present value which is -400,000. Negative sign is taken for pv as loan amount and payments have opposite cash flows.

=FV(0.005,360,1800,-400000)

=$600,903.01

Thus, $600,903 needs to be paid at the end as a balloon payment.