latoya wants to take out a home loan for $200,000. the interest rate is 4.75% per year and the loan term is…

Explanation:

Step1: Recall loan - payment formula

The formula for the monthly payment $M$ of a loan is $M = P\frac{r(1 + r)^n}{(1 + r)^n-1}$, where $P$ is the principal loan amount, $r$ is the monthly interest rate, and $n$ is the total number of payments. The principal $P=$200000$, the annual interest rate $i = 4.75%=0.0475$, so the monthly interest rate $r=\frac{0.0475}{12}$, and the loan term is 15 years, so the number of payments $n = 15\times12=180$.

Step2: Calculate the monthly payment

$r=\frac{0.0475}{12}\approx0.00395833$ $M = 200000\times\frac{0.00395833(1 + 0.00395833)^{180}}{(1 + 0.00395833)^{180}-1}$ First, calculate $(1 + 0.00395833)^{180}\approx2.01777$. $M = 200000\times\frac{0.00395833\times2.01777}{2.01777 - 1}$ $M = 200000\times\frac{0.007983}{1.01777}\approx1569.91$

Step3: Calculate the total amount to repay

The total amount to repay $A$ is the monthly payment times the number of payments. So $A = M\times n=1569.91\times180 = 282583.80$

Step4: Calculate the total interest paid

The total interest paid $I$ is the total amount to repay minus the principal. So $I=A - P=282583.80-200000 = 82583.80$

Answer:

(a) $$1569.91$ (b) $$282583.80$ (c) $$82583.80$