Question

You have just arranged for a $1,560,000 mortgage to finance the purchase of a large tract of land. the mortgage has an apr of 5.6 percent, and it calls for monthly payments over the next 30 years. however, the loan has an eight-year balloon payment, meaning that the loan must be paid off then. how big will the balloon payment be? (do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Answer 1

P=1560000
APR=5.6%
monthly interest, i=5.6%/12=7/1500  [fractions keep exact values]
R=1+i=1+7/1500
# of periods, n=30 years = 360 periods
monthly payment, A
A=PR^n(i)/(R^n-1)
=1560000*(1+7/1500)^360*(7/1500)/((1+7/1500)^360-1)
=$8955.632

At the end of eight years,
number of periods, n1 = 8*12 = 96

If paid off at the end of 8 years, value of loan then
future value of principal
F1=PR^n1=1560000*(1+7/1500)^96=2439135.635
future value of payments
F2=A(R^n1-1)/i=8955.632*(1+7/1500)^96-1)/(7/1500)=1081485.620
Therefore the balloon payment
= future value of principal (owing) - future value of payments (paid)
=F1-F2
=2439135.635-1081485.620
=1357650.0152
Round to two places after decimal to get final answer.