Question

jackson is looking to take out a 10-year mortgage from a bank offering an annual interest rate of 4.5%, compounded monthly using the formula below, determine the maximum amount jackson can borrow, to the nearest dollar, if the highest monthly payment he can afford is $ 2 , 775 $2,775.

Answer 1

To determine the maximum amount Jackson can borrow on a 10-year mortgage with a 4.5% annual interest rate, compounded monthly, we can use the present value formula. Plugging in the values of the monthly payment, interest rate, and loan term, we find that Jackson can borrow a maximum amount of $264,499.

Step-by-step explanation:

To determine the maximum amount Jackson can borrow on a 10-year mortgage, we can use the present value formula. The formula is:

Loan Amount = Monthly Payment * [1 - (1 + Monthly Interest Rate)^(-Total Number of Payments)] / Monthly Interest Rate

In this case, the monthly payment Jackson can afford is $2,775, the annual interest rate is 4.5%, compounded monthly, and the loan term is 10 years. To calculate the monthly interest rate, we divide the annual interest rate by 12, and then convert it to a decimal by dividing by 100. Plugging in the values, we get:

Monthly Interest Rate = 4.5% / 12 / 100 = 0.00375

Total Number of Payments = 10 years * 12 months per year = 120

Loan Amount = $2,775 * [1 - (1 + 0.00375)^(-120)] / 0.00375 = $264,499 (rounded to the nearest dollar)

Therefore, the maximum amount Jackson can borrow is $264,499.

Answer 2

To determine the maximum loan amount for a 10-year mortgage, the present value formula is used. The maximum loan amount Jackson can borrow is approximately $264,942, given an annual interest rate of 4.5% compounded monthly and a maximum monthly payment of $2,775.

Step-by-step explanation:

To determine the maximum amount Jackson can borrow for a 10-year mortgage, we need to use the present value formula. The formula for calculating the present value of a mortgage is:

PV = PMT × ((1 - (1 + r/n)^(-n*t))/(r/n))

Where:

• PV is the present value or the maximum loan amount
• PMT is the monthly payment
• r is the annual interest rate (as a decimal)
• n is the number of compounding periods per year
• t is the number of years

In this case, Jackson can afford a maximum monthly payment of $2,775, the annual interest rate is 4.5%, compounded monthly, and the loan term is 10 years. Plugging in these values into the formula, we have:

PV = 2775 × ((1 - (1 + 0.045/12)^(-12*10))/(0.045/12))

Calculating this equation, we find that the maximum loan amount Jackson can borrow is approximately $264,942.