Respuesta :
The first step is to calculate the payment, that is going to be equal for each month.
To do that, we apply the annuity equation:
[tex]C=P\cdot\frac{\frac{r}{m}}{1-\frac{1}{(1+\frac{r}{m})^{n\cdot m}}}[/tex]Where C is the total monthly payment, P is the principal (106,000), n is the number of years (20), m is the number of superiods (for monthly payments, is equal to 12) and r is the annual interest rate (6% or 0.06).
Then, we can calculate:
[tex]\begin{gathered} C=106,000\cdot\frac{\frac{0.06}{12}}{1-\frac{1}{(1+\frac{0.06}{12})^{20\cdot12}}} \\ C=106,000\cdot\frac{0.005}{1-\frac{1}{1.005^{240}}} \\ C=106,000\cdot\frac{0.005}{1-0.3} \\ C=106,000\cdot\frac{0.005}{0.7} \\ C=106,000\cdot0.00714 \\ C\approx757.14 \end{gathered}[/tex]The monthly payment is $757.14.
We can calculate the amount of interest that is paid by applying the simple interest formula:
[tex]I=\frac{r}{m}\cdot P=\frac{0.06}{12}\cdot106,000=0.005\cdot106,000=530[/tex]The interest payment is $530, so the difference between the total payment and the interest payment mst be the principal payment U:
[tex]U=C-I=757.14-530=227.14[/tex]This principal payment is deducted from the principal, so the balance of principal becomes (after the first payment):
[tex]P^{\prime}=P-U=106,000-227.14=105,772.86[/tex]Answer:
a) Total Payment: $757.14
b) Interest Payment: $530.00
c) Principal Payment: $227.14
d) Balance of Principal: $105,772.86
