Final answer:
The answer explains how to calculate the monthly deposit needed to reach the retirement goal and how to determine the interest earned over the 30-year period.
Explanation:
a) How much would you need to deposit in the account each month?
- Calculate the monthly interest rate: 5% / 12 = 0.4167%.
- Use the formula for calculating monthly deposits for a future value: Deposit = FV / ((1 + Monthly Interest Rate)^Total Months - 1) / Monthly Interest Rate) where FV = [tex]$300,000, Total Months = 30 years 12 months = 360 months.
- Plugging in the values: Deposit = $[/tex]300,000 / ((1 + 0.004167)^360 - 1) / 0.004167).
b) How much interest will you earn?
- To calculate the interest earned, subtract the total contribution made over 30 years from the total amount accumulated.
- Evaluate the total interest earned by subtracting the sum of deposits made from the final account balance.
- Interest Earned = Total Amount - (Monthly Deposit Total Months).
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