Final answer:
Sarah's estimated monthly payment for a $25,000 business loan with a 5.75% interest rate over 60 months is approximately $481.72, calculated using the loan amortization formula.
Step-by-step explanation:
The question pertains to the calculation of the estimated monthly payment for a small business loan using the loan amortization formula. Sarah has taken a loan for $25,000 with an interest rate of 5.75% to be repaid over 60 months. To calculate the monthly payment, we’ll use the formula for an amortizing loan, which can be expressed as:
A = P * (r(1+r)^n) / ((1+r)^n - 1)
Where:
- A = the monthly payment
- P = principal amount ($25,000)
- r = monthly interest rate (5.75% per year / 12 months = 0.00479167)
- n = total number of payments (60)
We then insert the values into the equation:
A = $25,000 * (0.00479167(1+0.00479167)^60) / ((1+0.00479167)^60 - 1)
After calculating, we find that the estimated monthly payment is approximately $481.72.
It's important to note that this calculation assumes a fixed interest rate for the entire repayment period, and does not account for any fees or penalties that may be applicable. This loan will help the borrower with their business financing needs, and understanding these payments is critical in planning for financial stability and success.