A woman wants to borrow $11,000 in order to buy a car. She wants to repay the loan by monthly installments for 5 years. If the interest rate on this loan is 7 1/2%

per year, compounded monthly, what is the amount of each payment? (Round your answer to the nearest cent.)

same question as the previous one,

let me know what you got

To find the amount of each monthly payment, we can use the formula for calculating the monthly payment on a loan:

P = (PV * r) / (1 - (1 + r)^(-n))

Where:
P = monthly payment
PV = present value of the loan (initial amount borrowed)
r = monthly interest rate (annual interest rate divided by 12)
n = total number of monthly payments (number of years multiplied by 12)

In this case:
PV = $11,000
r = 7.5% / 100 / 12 = 0.00625 (decimal representation of the monthly interest rate)
n = 5 years * 12 months/year = 60 monthly payments

Now, let's substitute these values into the formula and solve for P:

P = (11000 * 0.00625) / (1 - (1 + 0.00625) ^ (-60))

Using a calculator, we can calculate this as:

P ≈ $216.01

Therefore, the amount of each monthly payment would be approximately $216.01 (rounded to the nearest cent).

To find the amount of each monthly payment, you can use the formula for calculating the monthly payment on a loan called the amortization formula. The formula is:

P = (r * PV) / (1 - (1 + r)^(-n))

Where:
P = Monthly Payment
r = Monthly interest rate
PV = Present value or loan amount
n = Total number of months

In this case, the present value or loan amount (PV) is $11,000, the interest rate per year is 7 1/2% or 0.075, and the total number of months (n) is 5 years * 12 months/year = 60 months.

First, calculate the monthly interest rate (r) by dividing the annual interest rate by 12:

r = 0.075 / 12 = 0.00625

Now, plug in the values into the amortization formula:

P = (0.00625 * 11000) / (1 - (1 + 0.00625)^(-60))

Using a calculator, evaluate the expression on the right side of the equation:

P = (0.00625 * 11000) / (1 - (1 + 0.00625)^(-60))
P ≈ (68.75) / (1 - (1.00625)^(-60))
P ≈ (68.75) / (1 - 0.7050322)
P ≈ (68.75) / (0.2949678)
P ≈ 233.17

Rounded to the nearest cent, the amount of each monthly payment would be approximately $233.17.