Solve each of the following problems using the formulas for compound interest, the effective rate of interest, and the present and future values of annuities. Show your work, in particular how you start the problem: which equations you are using and where you are putting the variables.

The Garcia family would like to purchase a home. After examining their budget, they have decided that they could afford as much as $2,500 monthly mortgage payment. Assuming they can take out a 30-year mortgage at 5.2% interest compounded monthly, and assuming they have $20,000 in cash they intend to pay as a down payment, what is the highest price home they can afford to buy?