You want to have a $65,000 college fund in 10 years. How much will you have to deposit now under the scenario below. Assume that you make no deposits into the account after the initial deposit.
An APR of 6.7​% compounded daily
You should invest $____________________
​(Do not round until the final answer. Then round to two decimal places as​ needed.)

To determine how much you need to deposit now to have $65,000 in 10 years with an APR of 6.7% compounded daily, you can use the formula for the future value of a lump sum compounded periodically:

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

Where:
- $ A $ is the future value of the investment ($65,000),
- $ P $ is the present value or the amount to be deposited,
- $ r $ is the annual interest rate (6.7% or 0.067),
- $ n $ is the number of times the interest is compounded per year (daily compounding means $ n = 365 $),
- $ t $ is the number of years the money is invested (10 years).

We need to solve for $ P $:

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

Substitute the values:

\[
P = \frac{65,000}{\left(1 + \frac{0.067}{365}\right)^{365 \times 10}}
\]

Now let's calculate this.The amount you need to deposit now is approximately **$33,263.10** to have $65,000 in 10 years with an APR of 6.7% compounded daily.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How would the required deposit change if the interest rate were higher or lower?
2. What would be the effect of compounding monthly instead of daily?
3. How much interest will have been earned at the end of 10 years?
4. How much would you need to deposit for a shorter investment period, like 5 years?
5. What if you made additional yearly contributions to the account?

**Tip:** Understanding the difference between simple interest and compound interest can significantly affect your investment strategy!

Learn how to calculate the initial deposit required to achieve a $65,000 college fund in 10 years with a 6.7% annual interest rate compounded daily. Understand the compound interest formula and its application in financial planning.

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