We can solve this problem using the formula for the future value of an annuity (for recurring monthly payments into the IRA). The future value formula is given by:

$FV = P \times \frac{(1 + r)^n - 1}{r}$

Where:

• $FV$ = Future value (amount in the IRA after retirement)
• $P$ = Monthly deposit
• $r$ = Monthly interest rate
• $n$ = Total number of payments (months)

Given:

• Annual Percentage Rate (APR) = 44% → Monthly rate $r = \frac{44\%}{12} = 0.44 / 12 \approx 0.03667$
• Monthly deposit $P = 3535$
• Age when the account is set up = 20
• Retirement age = 65
• Number of years between 20 and 65 = 65 - 20 = 45 years
• Total number of months $n = 45 \times 12 = 540$

Part 1: Future Value (FV)

We will use the future value formula to calculate the total amount in the IRA at retirement.

Part 2: Total Deposits

The total deposits made are simply the monthly deposit multiplied by the total number of months: $\text{Total deposits} = P \times n$

Let's calculate both values.### Part 1: Future Value of the IRA At retirement, the IRA will contain approximately $26,868,938,669,919.77.

Part 2: Total Deposits

The total amount deposited into the account over the 45 years is $1,908,900.

Comparison

The future value of the IRA far exceeds the total deposits, illustrating the dramatic effect of compound interest over time, especially with a high APR like 44%.

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Would you like more details or have any further questions?

Here are 5 related questions you might find helpful:

1. How does changing the APR affect the future value of the IRA?
2. What would the future value be with a lower monthly deposit?
3. How much interest was earned over the entire period?
4. How would a different compounding frequency affect the results?
5. What is the impact of starting to save later, say at age 30?

Tip: Starting early with savings and compound interest significantly boosts long-term growth, especially with higher interest rates.