Question

Over the past 40 years, interest rates have varied widely. the rate for a 30-year mortgage reached a high of 14.75% in july 1984, and it reached 3.31% in november 2012. a significant impact of lower interest rates on society is that they enable more people to afford the purchase of a home. in the following exercise, we consider the purchase of a home that sells for $125,000. assume that we can make a down payment of $25,000, so we need to borrow $100,000. we assume that our annual income is $37,000 and that we have no other debt. if we can afford to pay a monthly amount of $613.33, 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

To determine how much we can borrow for a 30-year mortgage with an interest rate of 14.75%, we use a formula to calculate the monthly payment and rearrange it to solve for the loan amount. The maximum loan amount we can afford is approximately $62,970.

Step-by-step explanation:

To determine how much we can borrow for a 30-year mortgage with an interest rate of 14.75%, we need to calculate the monthly payment using the formula:

Monthly Payment = LoanAmount * (InterestRate/12) / (1 - (1 + InterestRate/12)^(-TermInMonths))

Plugging in the values, we get:

Loan Amount = $100,000

Interest Rate = 14.75% / 100 = 0.1475

Term = 30 * 12 = 360 months

Monthly Payment = $613.33

Now, rearranging the formula, we can solve for Loan Amount:

Loan Amount = Monthly Payment * (1 - (1 + InterestRate/12)^(-TermInMonths)) / (InterestRate/12)

Plugging in the values, we get:

Loan Amount = $613.33 * (1 - (1 + 0.1475/12)^(-360)) / (0.1475/12)

Calculating this, we find that the maximum loan amount we can afford is approximately $62,970.