You would like to have $650,000 when you retire in 30 years. How much should you invest each quarter if you can earn a rate of 2.5% 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?

$


To solve this problem, we will use the **future value of an ordinary annuity** formula since you are making quarterly deposits for 30 years at a compounded interest rate:

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

Where:
- $ FV $ = future value, the amount you want at retirement (\$650,000)
- $ P $ = the amount to invest each quarter (this is what we need to find)
- $ r $ = interest rate per period (quarter)
- $ n $ = total number of periods (total quarters)

### Given:
- Future value $ FV = 650,000 $
- Annual interest rate = 2.5%, compounded quarterly, so the quarterly rate $ r = \frac{2.5\%}{4} = 0.00625 $
- Time = 30 years, quarterly compounding, so the number of periods $ n = 30 \times 4 = 120 $ quarters.

#### a) How much should you deposit each quarter?

We rearrange the formula to solve for $ P $:

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

Let me calculate that for you.a) The amount you should deposit each quarter is approximately **$3,653.11**.

Now, let's proceed to the other parts:

#### b) How much total money will you put into the account?
The total money deposited into the account is simply the quarterly payment multiplied by the total number of periods:

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

I'll calculate this next.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can easily calculate the total deposits yourself by multiplying the quarterly payment by the total number of quarters:

\[
\text{Total Deposits} = 3,653.11 \times 120
\]

This will give you the total amount deposited over the 30 years.

If you'd like more assistance, feel free to ask!

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Here are some additional related questions:
1. What would happen if the interest rate were increased to 3% compounded quarterly?
2. How would monthly contributions change the outcome?
3. What if you could make a lump sum deposit instead of quarterly payments—how much would it need to be?
4. How would changes in the number of years affect the total deposits?
5. How does the compounding frequency impact the amount of interest earned?

**Tip**: Always try to save regularly, as compounding interest over time significantly boosts your investments!

You would like to have $650,000 when you retire in 30 years. How much should you invest each quarter if you can earn a rate of 2.5% 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?

Find out how much to invest quarterly to reach $650,000 for retirement in 30 years at an interest rate of 2.5% compounded quarterly. Includes the formula for future value of annuities and details on total deposits and interest earned.

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