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More maaaath help (business math/TVM solver)

Cyrus

Cyrus

Iron Chef - Master Emeritus
All right guys. Out of twenty questions, this is the last one I have left...and yet I don't get it at all. Please help! =[

***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 35 yr, and the interest rate was 12%/year compunded monthly on the unpaid balance. Because the interest rate for a conventional 35-year home mortgage has now dropped to 10%/year compounded monthly, Diane is thinking of refinancing her property. please round all answers to the nearest cent.

A) What is diana's current monthly mortgage payment?

***Right answer: 3351.31

B) What is Diana's current outstanding principal?

***Right answer: 325809.18

C) If diane decides to refinance her property by securing a 35-year home pmortgage loan in the amount of the current outstanding principal at the prevailing interest rate of 10%/year compounded monthly, what will be her monthly mortgage payment?

***Right answer: 2800.89

D) How much less would Diane's monthly mortgage payment be if she refinances?

***Right answer: 550.42


All help is MUCH appreciated...THANKS!!!
 
The "compounded monthly" thing throws this answer slightly.

Shampoo formula: Pe^(rt). This works for compounding continuously. I'm guessing that compounding monthly is simply a matter of changing e to some other constant.

If you're using a TI-83, there's a very useful application loaded onto the calculator that will figure all this out for you. Hit the "apps" button, then go to Finance, then TVM Solver. N is the number of time units you're working with. Some of the others should be obvious.
 
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Ketter I told you about P^ert the other day and you forgot about it :/
your book should have formulas for compounding other than continuous compounding.

 
For some reason banks divide the annual interest rate by 12 to arrive at the monthly interest rate when doing mortage calculations. (This benefits the banks so maybe it is not so strange :( )

The mortage has an interest component and a capital repayment component. But in order to keep the monthly payment constant the early years are predominately interest payments, very little of the capital is paid off. You can see this effect in the answer for B) The outstanding principle has hardly decreased even after paying $201,078.60
 
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homeofmew said:
? can you explain to me infinite series.
I get some of it but I have issues knowing which formula to use.
Click to expand...

Yup, everybody has issues with series.

If you're wondering how to test for convergence, I can't htink of anything easier but to use the first test that comes to mind.
 
For the loan, you need to work with the Present Value Annuity formula.

PV = pmt (1-(1+r/n)^(-nt))/(r/n)

In part a) PV = 330,000, r = .12, n = 12, t = 35. Solve for pmt.

for part b) pmt = answer from a. r = .12, n=12 and t = 30. Solve for PV (present value)

for part c) PV = answer from part b. r = .10, n = 12 and t = 35. Solve for pmt.

for part d) take answer from a minus answer from c.



The formula comes from the sum of a finite series. Do you want me to derive it for you? (I just finished covering this on Tuesday for the Finite Math for Business majors I am teaching.)
 
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