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.