Final answer:
To calculate the future value of a $50 monthly investment over 25 years at an 8% annual interest rate compounded monthly, the future value of an annuity formula is used. The formula accounts for regular deposits and compounding effects. A financial calculator or spreadsheet is typically used to obtain the exact figure due to the complexity of the calculation.
Step-by-step explanation:
To calculate the future value of regular deposits in an investment that earns compound interest, we use the future value of an annuity formula. Given a monthly deposit of $50, a monthly interest rate of 0.08/12 (annual rate divided by 12 months), over a period of 25 years (which is 300 months), we use the following formula:
FV = P × { ((1 + r)^n - 1) / r }
Where:
- FV is the future value of the annuity
- P is the monthly deposit ($50)
- r is the monthly interest rate
- n is the total number of deposits made over the period
By substituting the values into the formula, we can find the total amount accumulated after 25 years. Due to the complexity of the calculation, a financial calculator or spreadsheet software is commonly used to compute the exact total.