# Finite Math

Five years ago, Diane secured a bank loan of \$370,000 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% per year compounded monthly on the unpaid balance. Because the interest rate for a conventional 30-year home mortgage has now dropped to 6% per 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 balance?
\$

(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 6% per year compounded monthly, what will be her monthly mortgage payment? Use the rounded outstanding balance.
\$

(d) How much less would Diane's monthly mortgage payment be if she refinances? Use the rounded values from parts (a)-(c).
\$

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1. P = Po*r*t/(1-(1+r)^-t).
r = 0.1/12 = 0.00833/mo.
t = 30 * 12 = 360 mo.

P = 370,000*0.00833*360/(1-1.00833^(-360)) = \$1,168,458.50.
a. Monthly Payment(MP) = P/t = \$3245.72.

b. Bal. = P - 60*MP = \$973,715.30.

c. MP = Bal./t = \$2704.76.

d. 3245.72 - 2704.76 =

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