Answer:
It will take the same amount of time. 30 years.
Explanation:
First we need to know the mortgage value:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
monthly payment 2,006
time 360 (30 years x 12 months)
rate 0.003983333 (4.78%/12 months)
[tex]2006 \times \frac{1-(1+0.00398333333333333)^{-360} }{0.00398333333333333} = PV\\[/tex]
PV $383,221.4489
Then we solve for n if we make the payment twice as fast:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C $1,003.00
time n
rate 0.001991667 (4.78%/12 months / 2 payment per month)
PV $383,221.4489
As we are asked not to round up we post the full numbers
[tex]1003 \times \frac{1-(1+0.00199166666666667)^{-n} }{0.00199166666666667} = 383221.448870618\\[/tex]
[tex](1+0.00199166666666667)^{-n}= 1-\frac{383221.448870618\times0.00199166666666667}{1003}[/tex]
[tex]-n= \frac{log0.239033513791311}{log(1+0.00199166666666667)}[/tex]
-719.2851352
it will take 720 half month so:
720 / 2 = 360 months
360 monht 7 12 month per year = 30 years
It will take the same amount of time.
