Question

In the summer of 2014, the average listing price for homes for sale in the Hollywood Hills was $2,663,995.

a. Suppose you want to buy a home at that price with a 30-year mortgage at 5.25% annual interest, paying
10% as a down payment and with an annual escrow payment that is 1.2% of the full price of the home. What
is your total monthly payment on this house?
b. How much is paid in interest over the life of the loan?

Answer 1

• monthly payment: $15,903.61
• interest: $2,368,664.10

Explanation:

a) The loan amount is 90% of the price shown, so is ...

0.90 × $2,663,995 = $2,397,595.50

The monthly loan payment is given by the amortization formula:

A = P(r/12)/(1 -(1 +r/12)^(-12t))

A = $2,397,595.50(0.0525/12)/(1 -(1 +0.0525/12)^(-12·30))

A = $13,239.61

The monthly escrow payment will be 1/12 of the annual amount:

0.012 × $2,663,995 / 12 = $2664.00

So, the total monthly payment on the house will be ...

$13,239.61 +2664.00 = $15,903.61

__

b) The sum of monthly loan payments is ...

$13,239.61 × 360 = $4,766,259.60

so the interest on the $2,397,595.50 loan is ...

$4,766,259.60 -2,397,595.50 = $2,368,664.10