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The price of a home is $240,000. The bank requires 15% down payment. The buyer is offered two mortgage options: 15 year fixed at 6.5% or 30 year fixed at 6.5%. Calculate the amount of interest paid of each option? How much interest is saved with the 15 year option?

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An amount of $36 000 (`15/100 times 240 000 = 36 000` )is requried as the down payment. We must borrow $204 000. As we know the amount NOW we must use the present value formula:

`P_(v) = (x[1-(1+i)^(-n)])/i`

We know that `P_(v) = 204 000`

x is unknown

`i = 6.5% = 6.5/100 = 0.065`

which we divide by 12 (compounded monthly as not specified in the question but it is usual for mortgage bonds) `i=0.065/12`

`n= 15` years or `n=30` years which are x12 (due to compounding monthly.

now substitute...

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