Final answer:
The amount able to be borrowed with monthly payments of $300, at an annual interest rate of 5.1% compounded monthly for 5 years, is $16,810.38. The total interest paid over this period would be $1,189.62. The correct option was not provided in the given choices.
Step-by-step explanation:
To determine how much you are able to borrow with monthly payments of $300, an annual interest rate of 5.1% compounded monthly for 5 years, we use the formula for the present value of an annuity:
PV = Pmt × [(1 - (1 + r)^(-n)) / r]
Let's denote:
- PV = Present Value (amount of the loan)
- Pmt = Monthly payment ($300)
- r = Monthly interest rate (5.1% annual rate implies monthly rate = 5.1% / 12)
- n = Total number of payments (5 years × 12 months per year)
Given:
- Pmt = $300
- r = 5.1% / 12 = 0.425%
- n = 5 × 12 = 60
Plug the values into the formula:
PV = $300 × [(1 - (1 + 0.00425)^(-60)) / 0.00425]
PV = $300 × [(1 - (1 + 0.00425)^(-60)) / 0.00425] = $16,810.38
To calculate the total interest paid, we multiply the monthly payment by the total number of payments and subtract the amount borrowed:
Total interest = (Monthly payment × Total number of payments) - Amount borrowed
Total interest = ($300 × 60) - $16,810.38
Total interest = $18,000 - $16,810.38 = $1,189.62
The correct choice is not listed. However, based on our calculation, you would be able to borrow $16,810.38 and pay $1,189.62 in interest.