A couple just had a baby. How much should they invest now at 5.2​% compounded daily in order to have ​$50 comma 000 for the​ child's education 17 years from​ now? Compute the answer to the nearest dollar.​ (Assume a​ 365-day year.)
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Part 1
The couple should invest ​$
  
enter your response here now.
​(Round to the nearest dollar as​ needed.

To determine how much the couple should invest now, we can use the formula for compound interest:

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

Where:
- $ A $ is the amount of money to be accumulated (future value), which is \$50,000.
- $ P $ is the principal amount (initial investment) that we need to find.
- $ r $ is the annual interest rate, which is 5.2% or 0.052.
- $ n $ is the number of times the interest is compounded per year (daily compounding means $ n = 365 $).
- $ t $ is the time in years, which is 17 years.

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

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

Now let's compute the value of $ P $.The couple should invest **$20,658** now in order to have $50,000 for their child's education 17 years from now, with a 5.2% interest rate compounded daily.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How does daily compounding affect the final investment amount compared to annual compounding?
2. What if the interest rate were 6% instead of 5.2%? How much would the investment change?
3. How does the investment period (17 years) impact the initial investment required?
4. What would be the required investment if the goal was to accumulate $100,000 instead of $50,000?
5. How would the formula change if the interest was compounded monthly instead of daily?

**Tip:** The more frequently interest is compounded, the faster your investment grows due to the effects of "interest on interest."

A couple just had a baby. How much should they invest now at 5.2% compounded daily in order to have $50,000 for the child's education 17 years from now? Compute the answer to the nearest dollar. (Assume a 365-day year.)

Discover how to calculate the amount a couple needs to invest now at a 5.2% interest rate compounded daily, to save $50,000 for their child's education in 17 years. Detailed breakdown of the compound interest formula and step-by-step solution provided. Suitable for high school and college-level students.

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