Camden is looking to take out a mortgage for $\mathrm{\$}260,000$ from a bank offering an annual interest rate of $4.5\mathrm{\%}$, compounded monthly. Using the formula below, determine his monthly payment, to the nearest dollar, if the loan is taken over 10 years.
$$M=\frac{\mathrm{Pr}}{1-(1+r{)}^{-n}}$$
$M=$ the monthly payment
$P=$ the amount borrowed
$r=$ the interest rate per month
$n=$ the number of payments

Step 1 ：Given that the principal amount, P, is $260,000, the annual interest rate is 4.5%, and the loan is taken over 10 years.

Step 2 ：Since the interest is compounded monthly, we need to divide the annual interest rate by 12 to get the monthly interest rate, r. So, $r=\frac{4.5}{100\times 12}=0.00375$.

Step 3 ：The number of payments, n, is given as 10 years, but since payments are made monthly, we need to multiply this by 12. So, $n=10\times 12=120$.

Step 4 ：Substitute these values into the formula to calculate the monthly payment, M. So, $M=\frac{260000\times 0.00375}{1-(1+0.00375{)}^{-120}}$.

Step 5 ：Solving the above expression, we get M = 2695.

Step 6 ：Final Answer: The monthly payment, to the nearest dollar, if the loan is taken over 10 years is $\boxed{{\displaystyle 2695}}$.