Final answer:
To determine how much can be borrowed with a monthly payment of $613.33 over a 30-year term at 14.75% interest rate, use the present value of an annuity formula. The calculation accounts for a high interest rate, resulting in a lesser amount than at lower rates.
Step-by-step explanation:
When calculating how much can be borrowed with a monthly payment of $613.33, on a 30-year term at an interest rate of 14.75%, we must use the present value of an annuity formula. For a fixed-rate loan like a mortgage, the formula to calculate the present value, PV, which is the amount that can be borrowed, is given by:
PV = Pmt x [(1 - (1 + r)^-nt) / r]
Where Pmt is the periodic payment, r is the periodic interest rate (annual interest rate divided by 12), n is the number of payments per year (12), and t is the total number of years.
Using this formula, if we plug in the numbers for the given situation, we have:
PV = $613.33 x [(1 - (1 + 0.1475/12)^(-12*30)) / (0.1475/12)]
Calculating this gives a result, which can then be rounded to the nearest dollar to find out how much can be borrowed. With the high interest rate of 14.75%, this amount will be significantly less than one would expect with a lower interest rate, as shown in other provided examples.