Final answer:
To find out how much the Moreno family can borrow, we calculate the present value of an annuity using the formula PVA = PMT x [(1 - (1 + r)^-n) / r], with the given monthly payment, interest rate, and loan period.
Step-by-step explanation:
Calculating the Moreno Family's Affordable Mortgage
The question at hand involves determining the amount the Moreno family can borrow for a mortgage, given that they can afford a monthly payment of $2,600. To find this, we use the formula for the present value of an annuity, since a mortgage is essentially a series of monthly payments. The formula for the present value of an annuity (PVA) is PVA = PMT [ (1 - (1 + r)^-n) / r ], where PMT is the monthly payment, r is the monthly interest rate, and n is the total number of payments.
In the Moreno family's case, the annual interest rate is 5.25%, so the monthly interest rate is 5.25% / 12 months = 0.4375%. Converting this to a decimal for the formula, we get r = 0.004375. They want a 20-year mortgage, which means there will be n = 20 years x 12 months/year = 240 monthly payments. Inserting these values into the PVA formula gives:
PVA = $2,600 [ (1 - (1 + 0.004375)^-240) / 0.004375 ]
Calculating the above expression will give us the present value, which is the maximum loan amount the Moreno family can afford.