Answer
(a) $859.15$ dollars.
(b) $309,294.00$ dollars.
(c)$1,841,519.29$ dollars
Work Step by Step
Identify the given quantities: Loan $A_p=100000$, yearly interest $9.75\%$, compounded 12 times per year, number of years $30$
(a) We can get the interest per time period as $i=0.0975/12=0.008125$, and the total number of payments as $n=12\times30=360$, use the formula for monthly payment:
$R=\frac{iA_p}{1-(1+i)^{-n}}\frac{0.008125\times100000}{1-(1+0.008125)^{-360}}=859.15$ dollars.
(b) The total amount to be paid will be the product of monthly payment and the total times of payments:
$Total=Rn=859.15\times360=309294$ dollars.
(c) In this case, we have monthly deposit $R=859.15$, annual interest $9.75\%$, compounded monthly, total years $30$. Thus $i=0.0975/12=0.008125, n=12\times30=360$, and with the annuity formula
$A_f=R\frac{(1+i)^n-1}{i}=859.15\times\frac{(1+0.008125)^{360}-1}{0.008125}\approx1841519.29$ dollars
