Questions: Ethan starts an IRA (Individual Retirement Account) at the age of 26 to save for retirement. He deposits 300 each month. Upon retirement at the age of 65, his retirement savings is 916,785.09. Determine the amount of money Ethan deposited over the length of the investment and how much he made in interest upon retirement.
Transcript text: Ethan starts an IRA (Individual Retirement Account) at the age of 26 to save for retirement. He deposits $300 each month. Upon retirement at the age of 65, his retirement savings is $916,785.09. Determine the amount of money Ethan deposited over the length of the investment and how much he made in interest upon retirement.
Solution
Solution Steps
Step 1: Calculate the Total Investment Period
To find the total investment period, subtract the starting age from the retirement age: $Y = A_r - A_s = 65 - 26 = 39$ years.
Step 2: Calculate the Total Deposits Made
The total deposits made over the investment period is calculated by multiplying the total investment period in years by 12 (to convert to months) and then by the monthly deposit amount: $T = Y \times 12 \times D = 39 \times 12 \times 300 = 140400$.
Step 3: Calculate the Interest Earned
The interest earned upon retirement is found by subtracting the total deposits made from the final retirement savings: $I = S - T = 916785.09 - 140400 = 776385.09$.
Final Answer:
The total amount deposited into the IRA over the investment period is $140400$, and the interest earned upon retirement, rounded to 2 decimal places, is approximately $776385.09$.