Amir and Maite have a new grandson. How much money should they invest now so that he will have $75,000 for his college education in 18 years? The money is invested at 3.55% compounded monthly

To determine how much Amir and Maite need to invest now for their grandson to have $75,000 in 18 years, we use the formula for compound interest. Since the interest is compounded monthly, the formula is:

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

where:
- $A$ is the future value of the investment (the amount needed in the future),
- $P$ is the present value (the amount to be invested now),
- $r$ is the annual interest rate (in decimal form),
- $n$ is the number of times the interest is compounded per year,
- $t$ is the number of years.

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

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

Given:
- $A = 75,000$ dollars,
- $r = 3.55\%$ per annum or 0.0355 in decimal,
- $n = 12$ (compounded monthly),
- $t = 18$ years.

Substituting these values into the formula:

\[
P = \frac{75,000}{\left(1 + \frac{0.0355}{12}\right)^{12 \times 18}}
\]

Let's compute this.Amir and Maite should invest approximately **$39,623.86** now so that their grandson will have $75,000 for his college education in 18 years, assuming an interest rate of 3.55% compounded monthly.

Would you like more details or have any questions?

Here are 5 related questions that might interest you:
1. What happens if the interest rate changes to 4%?
2. How does changing the compounding frequency (e.g., quarterly) affect the investment amount?
3. What is the future value if they invest a different amount, like $50,000?
4. How much should they invest if they want $100,000 in 18 years?
5. How does inflation affect the future value of the investment?

**Tip:** Understanding the effect of compounding frequency can help in making better investment decisions.

Amir and Maite have a new grandson. How much money should they invest now so that he will have $75,000 for his college education in 18 years? The money is invested at 3.55% compounded monthly.

Learn how to calculate the present value of an investment for a future amount of $75,000 over 18 years with an interest rate of 3.55% compounded monthly. This problem uses the compound interest formula and is suitable for high school students in Grades 10-12.

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