Five years ago, Diane secured a bank loan of $360,000 to help finance the purcha

Question

Five years ago, Diane secured a bank loan of $360,000 to help finance the purchase of a loft in the San Francisco Bay area. The term of the mortgage was 30 yr, and the interest rate was 10%/year compounded monthly on the unpaid balance. Because the interest rate for a conventional 30-yr 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-yr 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 would Diane's monthly mortgage payment be if she refinances?

Explanation / Answer

The formula used to calculate the fixed monthly payment (P) required to fully amortize a loan of L dollars over a term of n months at a monthly interest rate of r is

P = L[r(1 + r)n]/[(1 + r)n - 1].

(a). Here, L=360000,n =30*12=360 and r=10/1200=1/120. Then P=(360000*1/120)[(1+1/120)360]/ [(1+1/120)360 -1] = 3000* 19.83739935/18.83739935 = $ 3159.26 (on rounding off to the nearest cent).Thus, Diane's current monthly mortgage payment is $ 3159.26.

(b). Since $ 360000/360 = $ 1000, the monthly reduction in the principal amount of loan is $ 1000. After 5 years, Diane's current outstanding principal is $ 360000- 5*12*1000 - $ 300000.

(c ). The formula used to calculate the remaining loan balance (B) of a fixed payment loan after p months is

B = L[(1 + r)n - (1 + r)p]/[(1 + r)n - 1]. Here, B = 360000[(121/120)360-(121/120)60 ]/[ (121/120)360-1] = 360000 *(19.83739935 – 1.645308934)/ 18.83739935 = $ 347667.55(on rounding off to the nearest cent).

If Diane decides to refinance her property by securing a 30-yr home mortgage loan in the amount of the current outstanding principal at the prevailing interest rate of 7%/year compounded monthly, then P = 347667.55*(7/1200)[(1+7/1200)360]/[(1+7/1200)360-1]=347667.55* (7/1200)*8.116497466/7.116497466 = $ 2313.04 (on rounding off to the nearest cent).

(d). Diane's monthly mortgage payment will be lower by $ 3159.26-$ 2313.04 = $ 846.22, if she refinances.

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