Question

If we can afford to pay a monthly amount of $753.33, determine how much we can borrow if the term is 30 years and the interest rate is at the historic high of 14.75%? (round your answer to the nearest dollar.)

Answer 1

By using the formula for the present value of an annuity, one can calculate that approximately $86,400 can be borrowed with a monthly payment of $753.33 at a 14.75% interest rate over 30 years.

Step-by-step explanation:

To determine how much can be borrowed with a monthly payment of $753.33 and an interest rate of 14.75% over a 30-year term, we use the formula for the present value of an annuity:

PV = PMT [1 - (1 + i)^(-n)] / i

In this scenario, PMT is the monthly payment of $753.33, i is the monthly interest rate, which we calculate by dividing the annual rate by 12 (0.1475 / 12 = 0.0122917), and n is the total number of payments over 30 years (30 * 12 = 360).

Substituting the values into the formula:

PV = 753.33 [1 - (1 + 0.0122917)^(-360)] / 0.0122917

When we compute this, PV equals approximately $86,399.59. Therefore, the amount that can be borrowed is $86,400 when rounded to the nearest dollar. The calculations here demonstrate how payment amounts, interest rates, and loan terms interact in the loan payment structure.