Final answer:
To find the future value of a loan at 7.57% annual simple interest for 17 months, calculate the simple interest and add it to the principal. Convert the time period to years and use the simple interest formula. Then compute the future value by adding the interest to the principal.
Step-by-step explanation:
To find the future value of the loan, we will calculate the simple interest first and then add it to the principal amount. The future value FV is given by FV = P + (P × r × t), where P is the principal amount, r is the annual interest rate in decimal form, and t is the time in years. Since we are given a time period in months, we need to convert it into years.
Let's calculate the simple interest and future value:
Principal (P) = $6365
Annual interest rate (r) = 7.57% or 0.0757
Time (t) in months = 17 months
Time (t) in years = 17/12 years
Simple Interest (SI) = P × r × t
SI = $6365 × 0.0757 × (17/12)
Now, let's compute the total future amount:
Future Value (FV) = Principal + Simple Interest