To calculate the amount in the account after 3 years and 9 months with monthly compounding interest, we use the formula for compound interest:

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

Where:

• $A$ is the final amount in the account,
• $P$ is the principal (initial investment) = $80,
• $r$ is the annual interest rate (as a decimal) = 2.5% = 0.025,
• $n$ is the number of times the interest is compounded per year = 12 (monthly),
• $t$ is the time in years = 3 years and 9 months = 3.75 years.

Now, let's calculate it step by step.

$A = 80 \left(1 + \frac{0.025}{12}\right)^{12 \times 3.75}$

First, I'll compute this.The amount in the account after 3 years and 9 months will be approximately $87.85.

Would you like further details on this calculation or have any questions?

Here are some related questions to explore:

1. How would the amount change if the interest rate was 3% instead of 2.5%?
2. What if the compounding period was quarterly instead of monthly?
3. How much interest did Taylor earn in this time?
4. How does compound interest compare to simple interest in this scenario?
5. How would the amount change if Taylor invested for 5 years instead of 3 years and 9 months?

Tip: The more frequently interest is compounded, the faster your investment grows.