At age

2020​,

someone sets up an IRA​ (individual retirement​ account) with an APR of

44​%.

At the end of each month he deposits

​$3535

in the account. How much will the IRA contain when he retires at age​ 65?  Compare that amount to the total deposits made over the time period.

Question content area bottom

Part 1

After retirement the IRA will contain

​$enter your response here.

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Part 2

The total deposits made over the time period is

​$enter your response here.

​(Type a whole​ number.)

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%.

---

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.

At age 20, someone sets up an IRA (individual retirement account) with an APR of 44%. At the end of each month, he deposits $3535 in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period.

This problem demonstrates how to calculate the future value of an IRA with a 44% APR and monthly deposits of $3535 over 45 years, using the compound interest formula for annuities. Learn how compound interest dramatically increases the account balance over time. Suitable for high school students (Grades 11-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation