Final answer:
Les will save $200 monthly with an additional 50% employer match, resulting in $300 monthly contributions to his retirement account. Over 30 years at an 8.25% average annual return rate, the future value of his retirement savings can be calculated using the future value of an annuity formula.
Step-by-step explanation:
Calculating Retirement Savings with Employer Match and Compound Interest
Les is planning to save $200 a month for retirement, with an employer contribution of $0.50 for every $1.00 saved. This means for every $200 Les saves, the employer will add an additional $100, resulting in a total monthly contribution of $300 to Les's retirement plan. Over 30 years, assuming an average return of 8.25% on his retirement savings, we can use the future value of an annuity formula to calculate the total amount in Les's retirement account.
The future value of an annuity formula is:
FV = P × {[(1 + i)^n - 1] / i}
where FV is the future value of the annuity, P is the annuity payment per period, i is the interest rate per period, and n is the number of payments.
By substituting Les's values we get:
FV = $300 × {[(1 + 0.0825/12)^(30 × 12) - 1] / (0.0825/12)}
To solve for FV, we would perform the calculations based on the formulas provided, which could be easily done with a financial calculator or spreadsheet software. This determination would give us the total amount saved in Les's retirement account after 30 years, assuming the rate of return and contributions remain constant.