Question

Some friends tell you they paid 25,404 down on a new house and are to pay $843 per month for 30 years. If interest is 4.5% compounded monthly, what was the selling price of the house?

How much interest will they pay in 30 years?

Answer 1

Selling price = $190003.206 and total interest paid is $135640.794

Explanation:

The down payment of house = $25404

Monthly payment = $834 per month.

Total number of years = 30 years = 30*12 = 360 months.

Interest rate compounded monthly = 4.5 % * 1/12 = 0.375% per month or 0.00375.

Now we have to calculate the selling price of house and total interest paid.

Loan amount = Present value of monthly payments.

`\text{Loan amount} = ( Monthly \ payment * [1- (1+r)^(-n)])/(r) \\= ( 834 * [1- (1+ 0.00375)^(-360)])/(0.00375) \\= 164599.206`

Selling price of house = 25404 + 164599.206 = 190003.206

Interest amount = total amount of installment – loan amount

Interest amount = 834*360 – 164599.206 = 135640.794 dollars.