Question

You have a 25-year $400.000 mortgage with a 3. rate of interest compounded more that you make my person what the free end of year 15 26 Mumble Choice S202 506 5206 506 SO O

Answer 1

Solution

The correct answer is 202506

PV of annuity = Annuity*[(1-(1/(1-r)^n))/r]

n= number of years

r=annual rate

Here rate is compounded monthly

Therefore PV of annuity = Monthly Annuity*[(1-(1/(1+r/12)^(n*12)))/(r/12)]

Here years =25,PV =400000, rate=.035

Therefore 400000=Monthly Annuity*[(1-(1/(1+.035/12)^(25*12)))/(.035/12)]

400000=Monthly Annuity*199.7509

Monthly annuity= Monthly payment=2002.494

Now

Since this is monthly annuity the present value of the annuity at year 15, discounted from year 25 will give the loan balance at year 15

Therefore PV of annuity = Monthly Annuity*[(1-(1/(1+r/12)^(n*12)))/(r/12)]

For finding PV at 15 year-end n will be 10 years

PV at year 15 end=2002.494*[(1-(1/(1+.035/12)^(10*12)))/(.035/12)]

=202505.6

Thus the correct answer is 202506

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