To find how much Phineas's investment will be worth after 5 years, we can use the compound interest formula:

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

Where:

• $A$ is the amount of money accumulated after $t$ years, including interest.
• $P$ is the principal amount (initial investment) = 400.
• $r$ is the annual interest rate (in decimal) = 3.17% = 0.0317.
• $n$ is the number of times the interest is compounded per year = 12 (monthly).
• $t$ is the time the money is invested for, in years = 5.

Let's calculate $A$:

$A = 400 \left(1 + \frac{0.0317}{12}\right)^{12 \times 5}$

Now, I'll compute the result.The value of Phineas's investment after 5 years will be 468.60.

Would you like further details or have any questions?

Here are some related questions you may find interesting:

1. What would be the final amount if the interest rate increased to 4%?
2. How much interest would be earned if the money was compounded annually instead of monthly?
3. What if Phineas withdrew $50 after 3 years—what would the final amount be after 5 years?
4. How would the final amount change if Phineas invested for 10 years instead of 5?
5. How much would Phineas need to invest to have $600 after 5 years at the same rate?

Tip: Compounding more frequently generally results in a higher final amount.