# Bus Finance

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You want to purchase a home. cost \$165,000. you have \$40,000 downpayment. you want to finance rest at 3.5% for 15 years. how much will monthly mortgage be? How much in total will you pay over the 15 years even counting the downpayment? I came up with payment of \$893.6 for first part. Again, I am not too sure if I am entering correctly into the calculator.

Bus Finance - Reiny, Friday, February 3, 2012 at 5:18pm

balance after downpayment = 125000
i = .035/12 = .002916666... (I stored in memory of calculator)
n = 180

125000 = paym (1 - 1.002916666..^-180)/.00291666
payment = 893.60 , you are correct.

take it from there, that was the hard part

Bus Finance - allison, Friday, February 3, 2012 at 7:35pm

to continue. it asks how much in total you will pay over the 15 years based on mortgage and down payment. I used the (893.60*12)(15)+40,000=200848.00. It then asks what portion of that is interest. I used the 200848.00FV 125000PV 180N with the I/YR=3.17%.

Bus Finance - Reiny, Friday, February 3, 2012 at 8:12pm

since we paid back a total of 200848 on the original loan of 165000, the difference, or 35848 must have been interest.

****this is where I am coming up with something not adding up. I would assume since we only borrowed the \$125,000 that we would not be actually paying interest on the \$40,000 we put down to bring the total down from \$165,000. I took the monthly payments (893.6*12)*3.5%=375.31. I took (375.31*12)(15 years) and came up with \$67555.80 for total interest.

• Bus Finance -

http://www.jiskha.com/display.cgi?id=1328305692

I have no idea why you are taking
893.60(12)(.035) to get 375.31
That would a "simple interest" calculation.
BUT, the composition of interest and repayment of the constant 893.60 is changing from month to month
e.g.
interest in 1st month = 125000(.035)/12 = 364.58
repayment = 893.60 - 364.58 = 529.02
balance at end of 1st month = 125000 - 529.02 = 124470.98

interest in 2nd month = 124470(.035)/12 = 363.04
repayment = 893.60 - 363.40 = 530.56
balance at end of 2nd month = 124470.98 - 530.56 = 23940.42

etc.

think of it this way:::
cost = 165000

what did he actually pay?
paid: 40000 + 893.60(180) = 200848.00

so the difference = 200848 - 165000 = 35848

If you only want to consider the actual loan of 125000, then the actual outlay would be
893.60(180) or \$160848
and the difference between 160848 and 125000 is 35848
in other words, the 40000 would not enter the picture

In actuarial math we would never ask the question "What is the total interest ?"
since the amounts of interest are accrued at different times so we can't just add them up (which is what we just did)
e.g.
Suppose Bill owes 4000 now and another 2000 three years from now.
It would be false to say that Bill owes \$6000 , without taking into consideration the time interval and the rate of interest.

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