Five years ago, Diane secured a bank loan of $330,000 to help finance the purcha
ID: 2722107 • Letter: F
Question
Five years ago, Diane secured a bank loan of $330,000 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 8% 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).
$
Explanation / Answer
(a) Calculation of Monthly Mortgage Payment :
Principal (P) = 330,000 Interest (i) = 8% = 8/12/100 = 0.00667, Term (t) = 30 years = 30*12 = 360
The formula, Monthly Payment = P * r * (1 + r )n / [ ( 1 + r ) n - 1 ]
After inserting the values in the above formula we get,
330000 * 0.00667 * (1 + 0.00667 )360 / [ ( 1 + 0.00667 ) 360 - 1 ]
330000 * 0.00667 * (1.00667 )360 / [ ( 1.00667 ) 360 - 1 ]
330000 * 0.00667 * 10.9487 / 9.9487
2,422.34
The Monthly Payment = $ 2,422.34
(b) Calculation of Outstanding Balance:
The loan is 5 years ago, that means Number of Monthly payments = 5 * 12 = 60
Total Payment = 60 * 2422.34 = 145,340.40
Out of the above, Principa Repayment = 16270 and Interest = 129,070
Therefore, Outstanding Balance Now = 330000 - 16270 = 313,730
(c) Revised Monthly Payment =
Principal (P) = 330,000 Interest (i) = 6% = 8/12/100 = 0.005, Term (t) = 30 years = 30*12 = 360
The formula, Monthly Payment = P * r * (1 + r )n / [ ( 1 + r ) n - 1 ]
After inserting the values in the above formula we get,
330000 * 0.005 * (1 + 0.005 )360 / [ ( 1 + 0.005 ) 360 - 1 ]
330000 * 0.005 * (1.005 )360 / [ ( 1.005 ) 360 - 1 ]
330000 * 0.005 * 6.0225/ 5.0225
$ 1978.52 or say 1978
The Revised Monthly Payment = $ 1,978
(d) The Difference betwen (a) and (c) = 2422 - 1978 = $ 444
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