You are buying a home for $360,000. If you make a down payment of $60,000 and take out a mortgage on the rest at 8.5% compounded monthly, what will be your monthly payment if the mortgage is to be paid off in 15 years

$2954.22

Explanation:

We are given a present value of $360000 which needs to be paid in the future for the mortgage of a house therefore we are further told that $60000 of down payment has been made so now we are required to pay $300000 as monthly installments for the next 15 years so this is a present value annuity problem as we will have future regular periodic payments that for a house mortgage so firstly to interpret this information properly we will use the present value annuity to find the monthly payments which the formula is as follows:

Pv = Cx[(1 -(1+i)^-n)/i]  

where C is the periodic payment we are looking for.

Pv is the present value for the home which is $300000 as a down payment of $60000 was made.

i is the interest rate which is 8.5%/12 as we are told it is compounded monthly.

n is the number of periods the in which the mortgage payments are made which is 15 years X 12 months =180 payments.

now we will substitute in the above mentioned formula :

$300000 = Cx[(1-(1+8.5%/12)^-180)/(8.5%/12)] now we will divide both sides with what multiplies C in brackets to solve for C

$300000/[(1-(1+8.5%/12)^-180)/(8.5%/12)] = C

$2954.218674 = C now we round off to two decimal places

C= $2954.22 which will be the monthly payment for this mortgage for 15 years every month.