A couple plans to save for their child's college education. What principal must be deposited by the parents when their child is born to have $65,000 when the child reaches the age of 18? Assume the money earns 7% interest compounded quarterly. (Round your answer to two decimal places.)

To solve this problem, we can use the compound interest formula, which is:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the future value (amount of money they want to have, in this case, $65,000),
- $ P $ is the principal (initial deposit) that we need to find,
- $ r $ is the annual interest rate (7% or 0.07),
- $ n $ is the number of times the interest is compounded per year (quarterly compounding means $ n = 4 $),
- $ t $ is the number of years the money is invested (18 years).

We need to solve for $ P $. Rearranging the formula:

\[
P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}
\]

Now, we can substitute the given values into the formula:

\[
P = \frac{65000}{\left(1 + \frac{0.07}{4}\right)^{4 \times 18}}
\]

Let me calculate this.The principal amount that must be deposited by the parents when their child is born to have $65,000 at the age of 18, with a 7% interest compounded quarterly, is approximately **$18,639.54**.

Would you like further details or have any other questions?

Here are 5 related questions to think about:
1. How would the required principal change if the interest rate were 6% instead of 7%?
2. What would be the principal if the money were compounded monthly instead of quarterly?
3. How much interest will the parents have earned after 18 years?
4. If the parents could only save for 15 years, how much more would they need to deposit initially?
5. How would the final amount change if the interest were compounded annually instead of quarterly?

**Tip:** The more frequently interest is compounded, the greater the final amount will be due to the effect of compounding.

A couple plans to save for their child's college education. What principal must be deposited by the parents when their child is born to have $65,000 when the child reaches the age of 18? Assume the money earns 7% interest compounded quarterly. (Round your answer to two decimal places.)

Find out how much principal a couple needs to deposit at 7% interest compounded quarterly to reach $65,000 in 18 years for their child's college fund. This detailed guide explains the compound interest formula and provides a step-by-step solution. Ideal for students in Grades 11-12 studying financial mathematics.

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