Answer:
$556063.77 is the balloon payment in order to finish the loan in 8 years.
Explanation:
Firstly we will use the Present value formula annuity to find how much will we pay on a monthly basis for the 30 year mortgage loan so we are given :
Pv the present value of the mortgage is $1800000
i which is the interest rate 7.8%/12 as there will be monthly payments
is the number of payments which are 30 x 12 = 360 payments
then we substitute on the formula Pv= C[(1-(1+i)^-n) /i]
we are looking for C the monthly payments
$1800000= C[(1-(1+(7.8%/12))^-360)/(7.8%/12)] now divide by the coefficient of C both sides to solve for C
$1800000/[(1-(1+(7.8%/12))^-360)/(7.8%/12)] = C
$12957.66= C
now if the monthly payment is $12957.66 we will find how much we will pay in 8 years which will be $12957.66 x 12 x 8 = $1 243 936.23 now if this amount is covered for 8 years then the balloon payment is $1800000 - $1243936.23 = $ 556063.77 which is the remaining amount in present value terms, this is the balloon payment to finish the mortgage in 8 years.
