Final answer:
The question involves financial mathematics, specifically calculating simple interest and future value for given principal amounts, interest rates, and time periods. Example calculations are provided to illustrate how to determine the rate from interest earned and the future value based on compound interest.
Step-by-step explanation:
The question posed relates to calculating different financial values associated with simple interest and future value determination.
For simple interest, the formula used is: Interest = Principal × rate × time. As an example, if the interest earned is $500 from a principal of $10,000 over 5 years, the rate can be calculated as: $500 = $10,000 × rate × 5, leading to a rate of 1%.
For future value, the formula: Total future amount = Principal × (1 + interest rate)time is used. For instance, an initial amount of $1,000 earning an interest rate of 2% over 5 years would amount to a future value of $1,104.08.
The question also made reference to payments from a firm for present and future years, where the future values are calculated using a formula taking into account the received amounts and the interest rate over a number of years.