To solve this, we calculate the future value of an annuity and the total deposits.

Step 1: Given information

1. Monthly deposit ($PMT$): $55
2. Annual interest rate ($r$): 6% (0.06 as a decimal)
3. Monthly interest rate ($i$): $0.06 / 12 = 0.005$
4. Number of years of deposits ($t$): $65 - 18 = 47$
5. Number of periods ($n$): $47 \times 12 = 564$

Step 2: Future Value of an Ordinary Annuity Formula

The formula for the future value ($FV$) of an ordinary annuity is: $FV = PMT \cdot \frac{(1 + i)^n - 1}{i}$ Substitute the values: $FV = 55 \cdot \frac{(1 + 0.005)^{564} - 1}{0.005}$

Step 3: Solve for $FV$

$(1 + 0.005)^{564} = 1.005^{564} \approx 10.467$ $FV = 55 \cdot \frac{10.467 - 1}{0.005} = 55 \cdot \frac{9.467}{0.005}$ $FV = 55 \cdot 1893.4 \approx 104,137$

Part 1: Future Value

The IRA will contain approximately: $FV = 104,137.00$

Step 4: Total Deposits

The total deposits are simply the monthly contribution times the number of months: $Total \, Deposits = PMT \cdot n = 55 \cdot 564 = 31,020$

Part 2: Total Deposits

The total deposits made over the time period are: $Total \, Deposits = 31,020$

Final Answer

1. The IRA will contain approximately $104,137.00.
2. The total deposits made over the time period are $31,020.

Would you like me to explain this calculation further or provide details on any step?

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Related Questions:

1. What would the IRA value be if the APR was increased to 8%?
2. How much interest is earned over the time period?
3. What is the effect of doubling the monthly deposit on the future value?
4. How would the final amount change if the person started at age 25 instead?
5. What is the equivalent annual interest rate (EAR) for the 6% APR?

Tip:

Small monthly contributions, when invested early, can grow significantly due to the power of compound interest over time!