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?

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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.

You Have a 25-Year $800,000 Mortgage with a 4