Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $22,000
 over the next 3
 years. What amount must be deposited quarterly into an account that earns 4.7%
 interest, compounded quarterly, in order to reach your goal? Round your answer to the nearest cent, if necessary.


To determine the quarterly deposit needed to reach your goal of saving $22,000 in 3 years, given an interest rate of 4.7% 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 you want, which is $22,000.
- $ P $ is the quarterly deposit (what we are solving for).
- $ r $ is the quarterly interest rate (annual interest rate divided by 4).
- $ n $ is the total number of quarters (years multiplied by 4).

### Step-by-step calculation:
1. The annual interest rate is 4.7%, so the quarterly interest rate is:

\[
r = \frac{4.7\%}{4} = \frac{0.047}{4} = 0.01175
\]

2. The total number of quarters in 3 years is:

\[
n = 3 \times 4 = 12
\]

Now, substitute into the formula for $FV$ and solve for $P$:

\[
22000 = P \times \frac{(1 + 0.01175)^{12} - 1}{0.01175}
\]

Let's calculate the value of $P$.The quarterly deposit required to reach your goal of $22,000 in 3 years, with a 4.7% interest rate compounded quarterly, is approximately **$1,717.85**.

Would you like a detailed explanation of the process, or do you have any further questions?

Here are 5 related questions for further practice:
1. How would the deposit change if the interest rate was 6% compounded quarterly?
2. What would the total amount saved be if you deposited $1,800 quarterly instead?
3. How much interest will be earned on the $22,000 over 3 years?
4. How would the calculation change if the interest was compounded monthly?
5. What if the savings goal was $30,000 over the same period?

**Tip:** The more frequent the compounding period (quarterly, monthly, etc.), the more interest you can earn on your deposits.

Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $22,000 over the next 3 years. What amount must be deposited quarterly into an account that earns 4.7% interest, compounded quarterly, in order to reach your goal? Round your answer to the nearest cent, if necessary.

Find out how to calculate the quarterly deposit needed to save $22,000 over 3 years with a 4.7% interest rate compounded quarterly. This solution includes step-by-step calculations using the future value of an ordinary annuity formula. Suitable for high school and college-level students.

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