Answer:
a. Mortgage amount = Present value of annuity of monthly payment
Present Value of annuity = P*PVAF(rate,time)
where P = monthly payment=?
t = time in months=30*12=360 months
r = interest rate = r= 0.08/12=0.006667
Calculation of PVAF(0.6667%,360)
PVAF(rate,time) = 1-(1+r)^-n]/r
PVAF(0.6667%,360) = [1-(1+0.006667)^-360]/0.006667
= [1-(1.006667)^-360]/0.006667
= [1-0.0.908568]/0.006667
= 0.908568/0.006667
= 136.2784
$310,000 = P*136.2784
$310000/136.2784 = P
$2,274.76 = P(monthly payment)
Monthly payment on existing loan = $2,274.76
b. Outstanding principle = Present value annuity of monthly payment for 25 years(300 months)
= $2274.76*PVAF(0.6667%,300months)
= $2274.76*129.5601
= $ 294,718.13
PVAF (0.6667%,300) can be calculated as above has been calculated
c) If Diane refinances, New monthly mortgage for new 30 year(360 month) loan on outstanding balance at 6.5% per year or 6.5%/12 =0.5417%
$294,718.13 = P*PVAF(0.5147%,360)
$294,718.13 = P*163.6826
$294718.13/163.6826 = P
$1,800.55 = P(monthly payment)
The new monthly payment will be $1800.55
d) Difference in monthly payment = Old monthly payment-new monthly payment
= $2274.76 - $1800.55
= $474.21
However the new mortgage is for 30 years from today.
