Question

You wish to take out a $200,000 mortgage. the yearly interest rate on the loan is 4%, and the loan is for 30 years. how much will your monthly payment be? round your answer to the nearest cent. do not round until you have calculated the final answer.

Answer 1

The monthly payment for a $200,000 30-year mortgage at 4% interest is $954.83, rounding the total paid over the course of the loan to $343,738.80.

Step-by-step explanation:

The monthly mortgage payment for a $200,000 loan at a yearly interest rate of 4% over 30 years can be calculated using the formula for an annuity. The monthly payment (R) is equal to the loan amount (P) times the monthly interest rate (i) divided by 1 minus the inverse of (1+i) to the power of the total number of payments (n). The monthly interest rate is the annual rate divided by 12, so i = 0.04/12. The total number of payments for a 30-year mortgage is n = 30 * 12.

Using the formula, we find that the monthly payment is:
R = P * i / (1 - (1+i)^-n)
R = 200,000 * (0.04/12) / (1 - (1+0.04/12)^(-30*12))
R = $954.83

The direct answer is $954.83 per month.

After 30 years, the total amount paid would be $954.83 * 12 * 30, which equals $343,738.80, significantly more than the original loan amount due to interest.