Question

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

Answer 1

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:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 1,500.00

time 240 (20 years x 12 months)

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

$1500 \times \frac{1-(1+0.005)^{-240} }{0.005} = PV$

PV $209,371.1575

Quota x number of cuotas - principal = total interest

1,500 x 240 - 209,371.16 = 150628.84

30 years mortgage

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 1,500.00

time 360

rate 0.005

$1500 \times \frac{1-(1+0.005)^{-360} }{0.005} = PV$

PV $250,187.4216

Quota x number of cuotas - principal = total interest

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