Question

You have contracted to buy a house for​ $250,000, paying​ $30,000 down and taking out a fully amortizing loan for the​ balance, at a​ 5.7% annual rate for 30 years. What will your monthly payment be if they make equal monthly installments over the next 30 years​ (to the nearest​ dollar)?

Answer 1

$ 1252

Step-by-step explanation:

Since we have been given the annual rate, but we have been asked for monthly payments, the first thing we should do is calculate the monthly rate.

R = (1+ APY) ^ 1/12 -1

Where:

R: monthly rate

APY: annual rate

R= (1+0.057)^1/12-1

R= 0.0046

Then, having monthly rate data, we can calculate the monthly payments. For that, we will use the formula for the present value of an ordinary annuity.

PMT= (P*R) / (1-(1+R)^(-n))

Where:

PMT: Monthly payments

R: monthly rate

P: Present value

n: Period

PMT= (220,000 * 0.0046) / (1-(1.0046)^-360))

PMT= 1,252