Five years ago, Diane secured a bank loan of $390,000 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 7% 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?
$ 2861.68
Correct: Your answer is correct.
(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 7% 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).
$
current monthly rate = .08/12 = .006666.... (I stored this number)
P( 1 - 1.006......^-360/.0066666..... = 390000
P = 28616.68 <------ your answer.
amount owing after 5 years:
= 390000(1.006666..^60) - 2861.68(1.0066666..^60 - 1)/.0066666...
= ...
this becomes the present value of a mortgage with 7% p.a. compounded monthly
so perform the same calculation you did to find the 2861.68
that is i = .07/12 , n = 12(15) = ..
take over
I assumed that she would simply finish her original 30 year mortgage.
Reading it again, it says she starts a new 30 year mortgage, so n = 30(12)
To calculate Diane's current monthly mortgage payment, we can use the loan amount, term, and interest rate.
(a) To find Diane's current monthly mortgage payment, we need to use the loan amount of $390,000, the term of 30 years, and the interest rate of 8% per year compounded monthly. We can use the following formula for calculating the monthly payment for a loan:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))
First, we need to convert the annual interest rate to a monthly rate by dividing it by 12 and then converting it to a decimal. So the monthly interest rate would be (0.08 / 12) = 0.0067.
Next, we need to calculate the number of payments by multiplying the number of years by 12. So the number of payments would be (30 * 12) = 360.
Now we can plug these values into the formula:
Monthly Payment = (390,000 * 0.0067) / (1 - (1 + 0.0067)^(-360))
By calculating the above expression, we get Diane's current monthly mortgage payment to be $2,861.68.
(b) To find Diane's current outstanding balance, we need to know the elapsed time and the payment history. However, the question does not provide this information. Therefore, we cannot calculate the 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, we would need to know the outstanding balance. Since we don't have this information, we cannot calculate the new monthly mortgage payment.
(d) Since we don't have the outstanding balance or the new monthly mortgage payment, we cannot determine how much less Diane's monthly mortgage payment would be if she refinances.