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Part 1

A couple just had a baby. 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 

1717 

years from​ now? Compute the answer to the nearest dollar.​ (Assume a​ 365-day year.)

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Part 1

The couple should invest 

​$enter your response here 

now.

​(Round to the nearest dollar as​ needed.) 

This problem involves calculating the present value (the amount to invest now) of a future sum using the formula for compound interest. Since the interest is compounded daily, we'll use the formula for compound interest:

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

Where:
- $ A $ is the future value (in this case, $35,000),
- $ P $ is the present value (the amount to invest now),
- $ r $ is the annual interest rate (5.35% or 0.0535),
- $ n $ is the number of times the interest is compounded per year (since it is compounded daily, $ n = 365 $),
- $ t $ is the time in years (17 years).

We want to find $ P $, the present value. Rearranging the formula to solve for $ P $:

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

Now, we can plug in the given values:

\[
P = \frac{35,000}{\left(1 + \frac{0.0535}{365}\right)^{365 \times 17}}
\]

Let me compute this.The couple should invest **$14,096** now in order to have $35,000 for their child's education 17 years from now, with an interest rate of 5.35% compounded daily.

Would you like further clarification or additional details?

Here are five related questions to expand on this:
1. How would the investment change if the interest was compounded monthly instead of daily?
2. What if the interest rate were 6% instead of 5.35%?
3. How much interest will the couple earn over the 17 years?
4. What is the difference in investment if the goal was $50,000 instead of $35,000?
5. How does the time period of 17 years affect the present value compared to a shorter period?

**Tip:** The more frequently interest is compounded, the greater the amount of interest accrued.

A couple just had a baby. How much should they invest now at 5.35% compounded daily in order to have $35,000 for the child's education 17 years from now? Compute the answer to the nearest dollar. (Assume a 365-day year.)

Find out how much a couple should invest now at 5.35% compounded daily to reach a $35,000 education fund in 17 years. This solution uses the compound interest formula and provides a step-by-step guide to calculate the present value, making it suitable for high school and college-level finance or algebra students.

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