Question

You have budgeted $1800 per month for a house payment, once again ignoring taxes, insurance, and any possible mortgage insurance. If you could have bought last year, the interest rate on a 30 year mortgage would have been about 3.5%. How much could you have borrowed on your budget last year?

Answer 1

As per the information is given in the question, it can be simply said that EMI of $1800 can be afforded each month at 3.5% per annum for 30 years and we have to identify amount borrowed.

To calculate the amount borrowed, we shall use the following formula of EMI :

EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

Where P = Amount Borrowed, R = Rate, N= No. of monthly installments

Now using given values, we shall derive the value of the amount borrowed with the help of the above equation :

EMI = $1800

P = X (assume)

R = 3.5% per annum / 12months = .0029176 per month

N = 30 Years * 12 per year = 360

EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

$1800 = [X*(3.5%/12)*(1+(3.5%/12))^360]/(1+(3.5%/12))^360

$1800 = .00832209X/1.8532872

X = $ 400851

Hence, the amount could be borrowed for 30 years at 3.5% per annum at payable at $1800 per month is $ 400851.