Question

You take out a 30-year mortgage to buy a house worth $415,000. The down payment is 17% and the annual interest rate is 3.5%. What are the monthly payments?

Answer 1

The monthly payments are $1,546.73

Step-by-step explanation:

The monthly payments can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value of the mortgage balance = Mortgage worth - (Mortgage worth * Percentage of down payment) = $415,000 - ($415,000 * 17%) = $415,000 - $70,550 = $344,450

P = Monthly payments = ?

r = Monthly interest rate return rate = 3.5% / 12 = 0.035 / 12 = 0.00291666666666667

n = number of months = 30 years * 12 months = 360

Substitute the values into equation (1) and solve for P, we have:

$344,450 = P * ((1 - (1 / (1 + 0.00291666666666667))^360) / 0.00291666666666667)

$344,450 = P * 222.694984964558

P = $344,450 / 222.694984964558

P = $1,546.73442715748

Approximating to 2 decimal places, we have:

P = $1,546.73

Therefore, the monthly payments are $1,546.73.