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A home buyer can afford to spend no more than $1500/month on mortgage payments. Suppose that the interest rate is 6%, that interest is compounded continuously, and that payments are also made continuously. (a) Determine the maximum amount that this buyer can afford to borrow on a 20-year mortgage; on a 30-year mortgage. (b) Determine the total interest paid during the term of the mortgage in each of the cases in part (a). 2Evangelista Torricelli (1608–1647), successor to Galileo as court

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TomShelby

Answer:

20 years mortgage:

maximum loan  $ 209, 371.16

interest paid     $  150,628.84

30 years mortage

maximum loan  $ 250,187.4216

interest paid     $  289,812.58

Explanation:

20 years mortgage:

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C 1,500.00

time 240 (20 years x 12 months)

rate 0.005 ( 6% annual / 12 months per year)

[tex]1500 \times \frac{1-(1+0.005)^{-240} }{0.005} = PV\\[/tex]

PV $209,371.1575

Quota x number of cuotas - principal = total interest

1,500 x 240 - 209,371.16 = 150628.84

30 years mortgage

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C 1,500.00

time 360

rate 0.005

[tex]1500 \times \frac{1-(1+0.005)^{-360} }{0.005} = PV\\[/tex]

PV $250,187.4216

Quota x number of cuotas - principal = total interest

1,500 x 360 - 250,187.42 = 289,812.58

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