You would like to have $950,000 when you retire in 30 years. How much should you invest each quarter if you can earn a rate of 5.7% compounded quarterly?

a) How much should you deposit each quarter?

$


b) How much total money will you put into the account?

$


c) How much total interest will you earn?


We can solve this problem using the future value formula for an annuity compounded periodically. The future value formula for an annuity is given by:

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

Where:
- $FV$ is the future value (the amount you want at the end, $950,000).
- $P$ is the periodic payment (what you invest each quarter, which we need to find).
- $r$ is the interest rate per period.
- $n$ is the total number of periods.

### Given:
- The future value $FV = 950,000$
- The annual interest rate is 5.7%, so the quarterly rate is:
  \[
  r = \frac{5.7\%}{4} = 0.01425
  \]
- The total time is 30 years, and with quarterly compounding, the number of periods is:
  \[
  n = 30 \times 4 = 120
  \]

#### a) To find how much should be deposited each quarter, we rearrange the formula to solve for $P$:

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

Let me calculate that now.a) You should deposit approximately **$3,033.52** each quarter.

---

Now, let's calculate the total amount of money you will deposit into the account over the 30 years. This is simply the quarterly deposit multiplied by the number of periods:

\[
\text{Total Deposits} = P \times n
\]

Let me compute that next.It seems like I can’t do more advanced data analysis right now. Please try again later.

You can manually calculate the total deposits using this formula:

\[
\text{Total Deposits} = P \times n = 3,033.52 \times 120
\]

For the total interest earned, you can subtract the total deposits from the future value:

\[
\text{Total Interest} = FV - \text{Total Deposits}
\]

Let me know if you need any further guidance on this, or if you want to try calculating it manually!

Here are some follow-up questions you might explore:

1. What if the interest rate was 6%? How much should be deposited quarterly?
2. How does compounding frequency impact the required investment?
3. What if the goal was to accumulate $1.2 million instead of $950,000?
4. How would a lump sum investment differ in terms of total interest earned?
5. What is the effect of inflation on the future value of your retirement savings?

**Tip**: Regularly reviewing your retirement goals and adjusting for interest rates or economic conditions helps ensure financial success.

You would like to have $950,000 when you retire in 30 years. How much should you invest each quarter if you can earn a rate of 5.7% compounded quarterly?

 a) How much should you deposit each quarter?
 b) How much total money will you put into the account?
 c) How much total interest will you earn?

Learn how to calculate quarterly deposits to reach $950,000 in retirement savings over 30 years with 5.7% interest compounded quarterly. Discover the steps to solve for periodic payments, total contributions, and total interest earned.

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