Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $25,000
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 amount that must be deposited quarterly to reach your goal of $25,000 in 3 years, with an interest rate of 4.7% compounded quarterly, we can use the formula for the future value of a series of periodic payments (an annuity):

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

Where:
- $FV$ is the future value you want, which is $25,000.
- $P$ is the periodic payment (the amount we want to find).
- $r$ is the periodic interest rate.
- $n$ is the total number of payments.

Given:
- Annual interest rate = 4.7%
- Quarterly interest rate $r = \frac{4.7\%}{4} = 0.01175$
- Number of years = 3
- Number of quarters in 3 years $n = 3 \times 4 = 12$

Now plug these values into the formula and solve for $P$:

\[
25000 = P \times \frac{(1 + 0.01175)^{12} - 1}{0.01175}
\]

Let's solve for $P$.The amount that must be deposited quarterly to reach your goal of $25,000 in 3 years, with an interest rate of 4.7% compounded quarterly, is approximately **$1,952.10** per quarter.

Would you like more details or have any questions?

Here are some related questions that might interest you:

1. How would the deposit amount change if the interest rate was different?
2. What would the amount be if the savings period was extended to 5 years?
3. How does compounding frequency affect the required deposit?
4. What if deposits were made monthly instead of quarterly?
5. How can we calculate the total interest earned over the 3 years?

**Tip:** Regularly reviewing your savings goals and the interest rates of your accounts can help you make the most of your investments!

Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $25,000 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.

Learn how to calculate the quarterly deposit required to save $25,000 over 3 years with an interest rate of 4.7%, compounded quarterly. This problem demonstrates key mathematical concepts like compound interest and the future value of annuities, ideal for high school students in Grades 10-12.

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