You have a 25-year $800,000 mortgage with a 4.5% rate of interest (compounded monthly) that you make monthly payments on. What is the balance of the loan at the end of year 16?

A) $393,292
B) $394,292
C) $395,292
D) $396,292
E) $397,292

To find the balance of the loan at the end of year 16, we first calculate the monthly payment using the loan formula for fixed-rate mortgages, then determine the remaining balance after 16 years of payments. The monthly payment can be calculated using the formula: $$PMT=P\times \frac{r(1+r{)}^n}{(1+r{)}^n-1}$$ where $P$ is the principal amount ($800,000), $r$ is the monthly interest rate (annual rate divided by 12, so 4.5%/12 = 0.375%), and $n$ is the total number of payments (25 years \times 12 months = 300 payments). Plugging in the values, we get the monthly payment amount. To find the balance after 16 years (or 192 payments), we adjust $n$ to reflect the remaining payments (108 payments left) and solve for the new principal $P$ , which represents the balance. The correct balance, after performing these calculations, is $394,292.