Final answer:
The duration it takes to pay off a loan with these specifics requires the use of the amortization formula and financial calculations, typically carried out with a financial calculator or spreadsheet software. Direct calculation with the information provided is not possible without additional tools.
Step-by-step explanation:
To determine how long it will take to settle a loan with a known principal amount, interest rate, and regular payments, one would typically use the amortization formula. The question asks about a loan of $45,000 at a 5.10% interest rate compounded monthly, with monthly payments of $1,800.
The amortization formula is not provided in the student's resources but is as follows:
- Calculate the monthly interest rate by dividing the annual rate by 12. In this case, 5.10% divided by 12 months gives a monthly rate of 0.425%.
- Find the number of payments by using the formula for the present value of an annuity.
Unfortunately, with the information given in the question, we cannot provide an exact number of months without the use of a financial calculator or an iterative method such as a spreadsheet model or software designed to handle amortization schedules.
However, typically the duration of the loan payment schedule can be found by using a financial calculator or an appropriate function in spreadsheet software, like the NPER function in Excel, which requires the following arguments: the interest rate per period (monthly), the payment amount, the present value of the loan, and, optionally, the future value of the loan (typically 0 for fully amortized loans).
By inputting the provided data, one can determine the number of months required to pay off the loan. It's important to consider that, similar to the scenario where a $300,000 loan ends up costing significantly more over time, the total cost of the original loan will be higher than the principal amount borrowed due to interest accumulation over the life of the loan.