Answer:
1) Monthly payments:
[tex]Payment=\$1,394.15[/tex]
2) Balance in ten years:
[tex]Balance=\$166,676.94[/tex]
Explanation:
1. What are the monthly payments?
The formula to compute the monthly payment of a loan is:
[tex]Payment=Loan\times \dfrac{r(1+r)^n}{(1+r)^n-1}[/tex]
Where:
Substitute and compute:
[tex]Payment=\$ 190,000\times \dfrac{r(1+(0.08/12))^{360}}{(1+(0.08/12))^{360}-1}[/tex]
[tex]Payment=\$1,394.15[/tex]
2. What would the loan balance be in ten years?
There is a formula to calculate the balance in any number of years:
[tex]Balance=Loan(1+r)^n-Payment\times \bigg[\dfrac{(1+r)^n-1}{r}\bigg][/tex]
Substitute with n = 10 × 12 and compute:
[tex]Balance=\$190,000(1+(0.08/12))^{(10\times 12)}-\$1,394.15\times \bigg[\dfrac{(1+(0.08/12))^{(10\times 12)}-1}{(0.08/12)}\bigg][/tex]
[tex]Balance=\$166,676.94[/tex]
