Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $29,000 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 solve this problem, we will use the formula for the **future value of an ordinary annuity**, which is:

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

Where:
- $A$ is the future value (the goal), which is $29,000.
- $P$ is the amount deposited each period (what we are trying to find).
- $r$ is the interest rate per period.
- $n$ is the total number of periods.

### Given Information:
- The interest rate is 5.9% annually, compounded quarterly.
- The goal is to save $29,000 in 6 years.
- Compounding quarterly means there are 4 periods per year.
- The total number of periods, $n$, is $6 \times 4 = 24$.
- The quarterly interest rate, $r$, is $\frac{5.9\%}{4} = \frac{0.059}{4} = 0.01475$.

### Substituting into the formula:

\[
29000 = P \times \frac{{(1 + 0.01475)^{24} - 1}}{0.01475}
\]

Now, we will calculate the value of the right-hand side and solve for $P$.The amount that must be deposited quarterly into the account is approximately **$1,015.85** in order to reach the goal of $29,000 in 6 years.

Would you like more details or have any other questions?

Here are five related questions you might explore:
1. How would the deposit amount change if the interest rate were higher?
2. What if you wanted to reach the goal in 5 years instead of 6?
3. How much total interest would you earn over the 6 years?
4. What happens if the compounding frequency is increased to monthly?
5. How can we adjust the formula for continuous compounding?

**Tip:** Compound interest grows faster the more frequently it compounds. Compounding quarterly accelerates savings more than annual compounding.

Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $29,000 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 $29,000 in 6 years with an account earning 5.9% interest, compounded quarterly. This solution uses the future value of an ordinary annuity formula and covers key financial concepts like compound interest and annuities.

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