To calculate the monthly mortgage payment for a $200,000, 15-year mortgage at 4.75% annual interest rate compounded daily, we can use the following formula:
M = P * (r/12) * (1 + r/12)^(12*n) / ((1 + r/12)^(12*n) - 1)
where:
M = monthly mortgage payment
P = principal amount (the amount borrowed), which is $200,000 in this case
r = annual interest rate, which is 4.75%
n = number of years of the mortgage, which is 15 years in this case
Plugging in the values, we get:
M = 200000 * (0.0475/12) * (1 + 0.0475/12)^(12*15) / ((1 + 0.0475/12)^(12*15) - 1)
Simplifying this equation, we get:
M = $1,529.99 (rounded to the nearest penny)
Therefore, the monthly mortgage payment for a $200,000, 15-year mortgage at 4.75% annual interest rate compounded daily is $1,529.99.