Diane secured a bank loan of $310,000 to help finance the purchase of a loft in

Question

Diane secured a bank loan of $310,000 to help finance the purchase of a loft in the San Francisco Bay area. The term of the mortgage was 30 years, and the interest rate was 10%/year compounded monthly on the unpaid balance. Because the interest rate for a conventional 30-year home mortgage has now dropped to 7%/year compounded monthly, Diane is thinking of refinancing her property. (Round your answers to the nearest cent.)
(a) What is Diane's current monthly mortgage payment?

(b) What is Diane's current outstanding principal?
$

(c) If Diane decides to refinance her property by securing a 30-year home mortgage loan in the amount of the current outstanding principal at the prevailing interest rate of 7%/year compounded monthly, what will be her monthly mortgage payment?
$

(d) How much less will Diane's monthly mortgage payment be if she refinances?
$

Explanation / Answer

a)
Payment = rP / (1- (1+r)^(-n)

r=0.10/12
P=310,000
n=30x12=360 payments

Payment = (0.10/12)(310000) / (1-(1+.10/12)^(-360))
= $2,720.47
---------------------
c)
Payment = rP / (1- (1+r)^(-n)

r=0.07/12
P=310,000
n=30x12=360 payments

Payment = (0.07/12)(310000) / (1-(1+.07/12)^(-360))
= $2,062.44
-----------
saved = (360)($2,720.47) - (360)($2,062.44)
=$236890.8

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