How much should they invest now at 5.35.3​% compounded daily in order to have ​$35 comma 00035,000 for the​ child's education 1818 years from​ now?

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

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

Where:
- $ A $ is the future value (the amount you want to have, which is \$35,000),
- $ P $ is the present value (the amount to be invested now, which we're solving for),
- $ r $ is the annual interest rate (5.35%, or 0.0535 as a decimal),
- $ n $ is the number of times the interest is compounded per year (daily compounding means $ n = 365 $),
- $ t $ is the number of years (18 years).

### Rearrange the formula to solve for $ P $:

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

Now we can plug in the values:
\[
P = \frac{35,000}{\left(1 + \frac{0.0535}{365}\right)^{365 \times 18}}
\]

Let me calculate that for you.The amount they need to invest now is approximately **$13,362.05** to have $35,000 in 18 years, with a 5.35% interest rate compounded daily.

Would you like more details on the calculation or have any other questions?

Here are five related questions you might find helpful:
1. How does daily compounding differ from annual compounding?
2. How would the investment change with a different interest rate?
3. What would the future value be if a larger initial investment was made?
4. How does changing the investment period affect the required initial investment?
5. How would monthly contributions impact the final amount?

**Tip:** Compounding more frequently results in a slightly higher final amount due to interest being calculated more often.

How much should they invest now at 5.35% compounded daily in order to have $35,000 for the child's education 18 years from now?

Discover how to calculate the present investment needed at a 5.35% daily compounded interest rate to accumulate $35,000 in 18 years. This problem covers compound interest calculations and is ideal for high school students learning about exponential growth and interest rates.

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