Question

Suppose you just purchase a new house for $550,000, with a 20% down payment. The mortgage has a 6.1 percent stated annual interest rate, compounded monthly, and calls for equal monthly payments over the next 30 years. Your first payment will be due in 1 month. However, the mortgage has an eight-year balloon payment, meaning that the balance of the loan must be paid off at the end of Year 8. Suppose there are no other transaction costs or finance charges. How much will your balloon payment be in eight years?

Answer 1

Loan amount=L=550000*(1-20%)=$440000

Interest rate per month=i=6.1%/12=0.00508333

Time period=n=30*12=360 months

Monthly payment=L*(A/P,0.00508333,360)

Let us calculate the interest factor

$(A.P,i,n)=\frac{i}{1-\frac{1}{(1+i)^{n}}}$

$(A.P,0.00508333,360)=\frac{0.00508333}{1-\frac{1}{(1+0.00508333)^{360}}}=0.00605995$

Monthly payment=440000*0.00605995=$2666.38

Now let us calculate the balance left after 8 years

Balance left=440000*(F/P,0.00508333,96)-2666.38*(F/A,0.00508333,96)

Let us calculate the interest factors

(F/P,0.00508333,96)=(1+0.00508333)^96=1.62704183

(1+i)n-1 (F/A,1,n) =
$(F/A,0.00508333,96)=\frac{(1+0.00508333)^{96}-1}{0.00508333}=123.35257135$

Balance left=440000*1.62704183-2666.38*123.35257135=$386993.58

So, balloon payment=$386,993.58