A couple just had a baby. How much should they invest now at 5.25.2​% compounded daily in order to have ​$45 comma 00045,000 for the​ child's education 1717 years from​ now? Compute the answer to the nearest dollar.​ (Assume a​ 365-day year.)
Question content area bottom
Part 1
The couple should invest ​$enter your response here now.
​(Round to the nearest dollar as​ needed.) 

To solve this, we need to use the formula for compound interest:

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

Where:
- $A$ is the future value (the amount of money we want in the future, $45,000),
- $P$ is the present value (the amount of money to invest today, which we need to find),
- $r$ is the annual interest rate (5.252%, or 0.05252 in decimal form),
- $n$ is the number of times the interest is compounded per year (365 for daily compounding),
- $t$ is the time in years (17 years).

We are solving for $P$, so we rearrange the formula to solve for $P$:

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

Substitute the values:

- $A = 45,000$
- $r = 0.05252$
- $n = 365$
- $t = 17$

Now we can calculate this. Let's compute it.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can easily calculate the required investment using the formula I provided earlier.

If you need further guidance or clarification, feel free to ask!

Here are 5 related questions for further exploration:
1. How does daily compounding differ from monthly or annual compounding?
2. How would the required investment change if the interest rate were higher or lower?
3. What if the compounding were semi-annual instead of daily?
4. How does the formula for compound interest change with different time periods?
5. What would be the effect of starting the investment a few years later?

**Tip:** For more frequent compounding, the total interest earned will be slightly higher, resulting in a lower initial investment needed to reach the same future value.

A couple just had a baby. How much should they invest now at 5.25% compounded daily in order to have $45,000 for the child's education 17 years from now? Compute the answer to the nearest dollar.​ (Assume a​ 365-day year.)

Learn how to calculate the required investment amount to reach $45,000 in 17 years at an interest rate of 5.25% compounded daily. This problem involves using the compound interest formula, suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation