Final answer:
The monthly payment for the $160,000 mortgage over 25 years at 5.95% APR is calculated using the formula for monthly payment with values for principal, monthly interest rate, and number of payments plugged in. It is then computed and rounded to the nearest cent.
Step-by-step explanation:
To calculate the monthly payment of a $160,000 mortgage with a 25-year term and an APR of 5.95% based on monthly compounding, we use the formula for the monthly payment (M), which is M = P[r(1+r)^n] / [(1+r)^n-1], where P is the principal amount ($160,000), r is the monthly interest rate (APR divided by 12), and n is the total number of payments (25 years times 12 months).
First, we convert the APR to a monthly interest rate by dividing 5.95% by 12, which gives us 0.495833% or 0.00495833 in decimal form. Next, we'll calculate the total number of payments, which is 25 years multiplied by 12 months, resulting in 300 payments.
Plugging these values into the formula, we get: M = $160,000[0.00495833(1+0.00495833)^300] / [(1+0.00495833)^300-1]. After calculating this using a calculator or financial software, we round it to the nearest cent to find the monthly payment.