Suppose you want to have $400,000 for retirement in 20 years. Your account earns 8% interest. Round your answers to the nearest cent.

a) How much would you need to deposit in the account each month?
$
b) How much interest will you earn?

To determine how much you need to deposit each month and how much interest you will earn, we'll use the formula for the future value of an annuity:

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

Where:
- $FV$ = future value (the desired amount, $400,000)
- $P$ = monthly deposit
- $r$ = annual interest rate (8% or 0.08)
- $n$ = number of times the interest is compounded per year (monthly, so 12)
- $t$ = number of years (20 years)

### Part (a): How much would you need to deposit each month?

We need to rearrange the formula to solve for $P$ (monthly deposit):

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

Let me calculate the monthly deposit.The monthly deposit you would need to make is approximately **$679.09**.

### Part (b): How much interest will you earn?

To find the interest earned, we first calculate the total amount you will have deposited over 20 years and then subtract that from the future value:

\[
\text{Total Deposits} = P \times n \times t
\]
\[
\text{Interest Earned} = FV - \text{Total Deposits}
\]

Let's calculate the interest.The total interest you will earn over 20 years is approximately **$237,017.53**.

### Summary:
- **Monthly Deposit:** $679.09
- **Total Interest Earned:** $237,017.53

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:
1. What if the interest rate were 10% instead of 8%?
2. How would the monthly deposit change if you wanted to retire in 25 years instead of 20?
3. What if you wanted to accumulate $500,000 instead of $400,000?
4. How does compounding annually versus monthly affect the final amount?
5. What happens if you skip a few monthly payments during the 20-year period?

**Tip:** The earlier you start saving, the less you need to deposit monthly due to the power of compound interest.

Suppose you want to have $400,000 for retirement in 20 years. Your account earns 8% interest. Round your answers to the nearest cent.

a) How much would you need to deposit in the account each month?
$ 
b) How much interest will you earn?

Find out how much you need to deposit each month to reach $400,000 for retirement in 20 years with an 8% interest rate. Learn how compound interest works and calculate total interest earned over time. Suitable for Grades 10-12.

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