If $ 8000 is deposited in an account at the end of every quarter for the next 8 years, how

much will be in the account at the time of the final deposit if interest is 18% compounded

quarterly?

To calculate the future value of the account after making regular quarterly deposits of $8,000 for 8 years, with an interest rate of 18% compounded quarterly, we can use the **future value of an ordinary annuity** formula:

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

Where:
- $ FV $ is the future value of the annuity (the amount in the account after 8 years),
- $ P $ is the deposit made at the end of each period (in this case, $8,000),
- $ r $ is the interest rate per period,
- $ n $ is the total number of periods.

### Step 1: Define the variables

- $ P = 8,000 $ (quarterly deposit),
- The annual interest rate is 18%, so the quarterly interest rate $ r = \frac{18\%}{4} = 0.045 $,
- The total number of periods $ n = 8 \times 4 = 32 $ quarters (since there are 4 quarters in a year).

### Step 2: Substitute the values into the formula

\[
FV = 8,000 \times \frac{(1 + 0.045)^{32} - 1}{0.045}
\]

Now, let's calculate this.The future value of the account at the time of the final deposit will be approximately **$549,329.96**.

Would you like any further explanation on the steps involved, or do you have any other questions?

Here are five related questions you might find interesting:
1. What if the interest rate were compounded monthly instead of quarterly?
2. How would the future value change if the deposit amount were different?
3. What happens if the deposits are made at the beginning of each quarter instead of the end?
4. How can the formula be adapted for continuous compounding?
5. What is the difference between the future value of an ordinary annuity and an annuity due?

**Tip:** To maximize returns, always be aware of how frequently interest is compounded, as more frequent compounding increases the total future value.

If $8000 is deposited in an account at the end of every quarter for the next 8 years, how much will be in the account at the time of the final deposit if interest is 18% compounded quarterly?

Calculate the future value of quarterly deposits of $8000 over 8 years with an interest rate of 18% compounded quarterly. This step-by-step solution explores key financial concepts such as the future value of annuities and compound interest. Learn how to apply these concepts to maximize savings.

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