Answer
(a) $80487.84$ dollars.
(b) $603.66$ dollars, $120.51$ dollars.
Work Step by Step
Identify the given quantities: mortgage $A_p=90000$, interest rate $r=0.09$, over $30$ years, monthly payment $R=724.17$, $i=r/12=0.0075$
(a) After paying for 10 years, they will have 20 years remaining or $n_1=20\times12=240$ and the remaining balance is the present value of the 240 remaining payments, thus we have:
$A_p'=R\frac{1-(1+i)^{-n_1}}{i}=724,17\times\frac{1-(1+0.0075)^{-240}}{0.0075}\approx80487.84$ dollars.
(b) They will pay $i=0.0075$ of the remaining principal as interest for the next month, thus the interest would be $I=0.0075\times 80487.84\approx 603.66$ dollars. The difference of this value and the monthly payment would go toward the principal, that is $R-I=724.17-603.66=120.51$ dollars.
