Final answer:
To calculate the future value of $725 saved each year for 7 years at a 5% interest rate, the future value annuity formula is used. After calculating the FVA factor to be approximately 8.142 and multiplying it by $725, the future value is found to be approximately $5,903.05.
Step-by-step explanation:
The question pertains to the calculation of the future value of a series of annual savings using the concept of compound interest. To find the future value of $725 saved each year for 7 years at a 5 percent interest rate, the future value annuity formula needs to be applied:
Future Value Annuity (FVA) = P × { {(1 + r)^n - 1} / r }
Where P is the annual payment ($725), r is the annual interest rate (0.05, or 5%), and n is the number of periods (7 years).
First, calculate the FVA factor:
FVA factor = {(1 + 0.05)^7 - 1} / 0.05
After calculating the FVA factor (which should be around 8.142 after rounding to three decimal places), we multiply it by the annual payment:
Future Value = $725 × 8.142
Rounding the result to two decimal places, the future value of the annuity is:
Future Value = $5,903.05
This is the total amount that will be accumulated at the end of 7 years, taking into account the power of compound interest.