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))
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.
