Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $26,000
over the next 6
years. What amount must be deposited quarterly into an account that earns 5.9%
interest, compounded quarterly, in order to reach your goal? Round your answer to the nearest cent, if necessary.

To find the amount that must be deposited quarterly, we use the formula for the future value of an ordinary annuity, which is:

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

Where:
- $FV$ is the future value (the amount you want to save, $26,000).
- $P$ is the regular quarterly deposit.
- $r$ is the interest rate per quarter.
- $n$ is the total number of quarters.

### Step 1: Identify the variables
- The future value $FV = 26,000$
- The annual interest rate is 5.9%, but since it's compounded quarterly, we need to divide it by 4 to get the quarterly rate:  
  \[
  r = \frac{5.9\%}{4} = \frac{0.059}{4} = 0.01475
  \]
- The total number of quarters in 6 years is:  
  \[
  n = 6 \times 4 = 24
  \]

### Step 2: Solve for $P$
Rearrange the formula to solve for $P$:
\[
P = \frac{FV}{\frac{(1 + r)^n - 1}{r}}
\]

Substituting the known values:
\[
P = \frac{26,000}{\frac{(1 + 0.01475)^{24} - 1}{0.01475}}
\]

Now, let's calculate this.The quarterly deposit needed to save $26,000 over 6 years, with a 5.9% interest rate compounded quarterly, is approximately $910.76.

Would you like further details or have any questions?

Here are some related questions:
1. How does increasing the interest rate affect the required quarterly deposit?
2. What would happen if you made monthly instead of quarterly deposits?
3. How is the compounding frequency affecting your total savings over time?
4. How much total interest would you earn by the end of the 6 years?
5. What if the time frame to save for the car was reduced to 5 years?

**Tip:** Regular deposits into high-interest accounts can significantly grow your savings over time due to the power of compounding.

Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $26,000 over the next 6 years. What amount must be deposited quarterly into an account that earns 5.9% interest, compounded quarterly, in order to reach your goal? Round your answer to the nearest cent, if necessary.

Find out how much you need to deposit quarterly to save $26,000 in 6 years, with 5.9% interest compounded quarterly. This problem covers the future value of an ordinary annuity formula and explains how compound interest affects savings. Suitable for high school students learning financial mathematics.

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