Final answer:
To find out how much a couple can afford to borrow on a 30-year fixed-rate mortgage at 4.5% interest with $1,600 monthly payments, the present value of an annuity formula is used. By substituting the appropriate values into the formula, one can calculate the total loan amount they can afford.
Step-by-step explanation:
To determine how much the couple can afford to borrow with a 30-year fixed-rate loan at a 4.5% annual interest rate, compounded monthly, with a monthly payment of $1,600, we can use the present value of an annuity formula:
PV = PMT × ((1 - (1 + r)^{-n}) / r)
Where:
- PV is the present value, i.e., the amount they can afford to borrow.
- PMT is the monthly payment, which is $1,600.
- r is the monthly interest rate (annual rate divided by 12).
- n is the total number of payments (loan terms in years times 12).
In this case, r = 4.5% / 12 months = 0.375% per month, and n = 30 years × 12 months/year = 360 payments.
Plugging the numbers into the formula, we get:
PV = $1,600 × ((1 - (1 + 0.00375)^{-360}) / 0.00375)
After calculating the above expression, you will get the present value that represents how much the couple can afford to borrow, rounded to the nearest dollar.