Answer
30 year mortgage: $\$ R=643.70$
15 year mortgage: $\$ R=811.41$
Work Step by Step
(see p. 870)
If a loan $A_{p}$ is to be repaid in
$n$ regular equal payments with
interest rate $i$ per time period,
then the size $R$ of each payment is given by
$R=\displaystyle \frac{iA_{p}}{1-(1+i)^{-n}}$
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$A_{p}=80,000$,
monthly = 12 times per year,
$i=\displaystyle \frac{0.09}{12}=0.0075$.
Over a $30$ year period,
$n=30(12)=360$,
$R =\displaystyle \frac{(0.0075)(80,000)}{1-(1.0075)^{-360}}= \$ 643.70.$
Over a 15 year period,
$n=15( 12)=180$,
$R =\displaystyle \frac{80,000\cdot 0.0075}{1-(1.0075)^{-180}}=\$ 811.41$.
