Final answer:
To find the future value of the ordinary annuity, we convert the annual interest rate to a monthly rate, use the future value annuity formula, plug in the values, and calculate to find the total future value.
Step-by-step explanation:
To calculate the future value of an ordinary annuity with $115 monthly payments and a 5(3/4)% interest rate over one year, there are a few steps:
- First, convert the annual interest rate to a monthly rate. Since the interest rate is 5(3/4)%, or 5.75%, we divide this by 12 (months) to get the monthly interest rate.
- Then, use the future value annuity formula: Future Value of Annuity = Pmt × {[(1 + r)^n - 1] / r}, where Pmt is the monthly payment, r is the monthly interest rate, and n is the total number of payments.
- As this is a one-year annuity, n equals 12 (months).
- After plugging in the values, perform the calculations to find the total future value.
This process allows us to understand the compound interest on the monthly payments to determine the total future amount.