At age 25​, someone sets up an IRA​ (individual retirement​ account) with an APR of 5​%. At the end of each month he deposits ​$20 in the account. How much will the IRA contain when he retires at age​ 65?  Compare that amount to the total deposits made over the time period. 
Question content area bottom
Part 1
After retirement the IRA will contain ​$______.
(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 ​$_____.
(Type a whole​ number.)

This problem involves calculating the future value of an annuity. The individual is making monthly deposits of $20 into an IRA that earns 5% APR, compounded monthly. The total duration of investment is 40 years (from age 25 to 65).

### Part 1: Future Value of the IRA

The formula for the future value of an annuity compounded monthly is:

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

Where:
- $FV$ is the future value (what we are calculating),
- $P$ is the monthly deposit (\$20),
- $r$ is the annual interest rate (5% or 0.05),
- $n$ is the number of times the interest is compounded per year (12, since it's monthly),
- $t$ is the number of years the money is invested (40 years).

Substitute the given values into the formula:

\[
FV = 20 \times \frac{(1 + \frac{0.05}{12})^{12 \times 40} - 1}{\frac{0.05}{12}}
\]

### Part 2: Total Deposits Made

The total amount deposited is simply the monthly deposit times the number of months:

\[
\text{Total deposits} = 20 \times 12 \times 40
\]

Let's calculate both values.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can still proceed by using the formula provided to calculate the future value and total deposits manually or with a calculator. 

Here’s a quick summary of the steps:

1. **Future Value (FV)**:  
   \[
   FV = 20 \times \frac{(1 + \frac{0.05}{12})^{12 \times 40} - 1}{\frac{0.05}{12}}
   \]
   Plug in the values to compute the future value.

2. **Total Deposits**:  
   \[
   \text{Total deposits} = 20 \times 12 \times 40 = 9,600
   \]

Let me know if you'd like additional help with anything else!  

### Here are some related questions you might want to explore:
1. What happens to the final value if the interest rate increases to 6%?
2. How would the outcome change if deposits were made weekly instead of monthly?
3. If the individual starts depositing $50 a month, how much would the IRA contain at age 65?
4. What if the interest was compounded quarterly instead of monthly?
5. How does inflation affect the value of the amount at retirement?

### Tip:
Starting early with regular deposits in an IRA makes a big difference due to the power of compound interest!

At age 25​, someone sets up an IRA​ (individual retirement​ account) with an APR of 5​%. At the end of each month he deposits ​$20 in the account. How much will the IRA contain when he retires at age​ 65? Compare that amount to the total deposits made over the time period. Part 1: After retirement the IRA will contain ​$______. (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 ​$_____. (Type a whole​ number.)

Discover how to calculate the future value of an IRA with monthly deposits of $20 over 40 years at a 5% APR. This detailed guide walks you through the compound interest formula and the future value of an annuity, helping you understand exponential growth in finance. Learn how much the IRA will contain at retirement and compare it to the total deposits made. Suitable for high school seniors and college students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation