To solve this problem, we will calculate the principal for each account using the simple interest formula:

$I = P \cdot r \cdot t$ where:

• $I$ = interest earned,
• $P$ = principal (unknown),
• $r$ = annual interest rate (as a decimal),
• $t$ = time in years.

Step 1: Solve for $P$ in the formula

Rearranging for $P$:

$P = \frac{I}{r \cdot t}$

Step 2: Account A

• $I = 8.10$,
• $r = 3.6\% = 0.036$ (convert percent to decimal),
• $t = 18 \, \text{months} = \frac{18}{12} = 1.5 \, \text{years}$.

Substitute into the formula:

$P = \frac{8.10}{0.036 \cdot 1.5}$

Simplify:

$P = \frac{8.10}{0.054} \approx 150$

The principal for Account A is $150.

Step 3: Account B

• $I = 22.50$,
• $r = 2.5\% = 0.025$,
• $t = 27 \, \text{months} = \frac{27}{12} = 2.25 \, \text{years}$.

Substitute into the formula:

$P = \frac{22.50}{0.025 \cdot 2.25}$

Simplify:

$P = \frac{22.50}{0.05625} \approx 400$

The principal for Account B is $400.

Step 4: Which account earned more interest in the first month?

To determine this, calculate the interest earned per month for both accounts:

1. Account A:

   • Monthly interest = $\frac{I}{t \cdot 12} = \frac{8.10}{18} = 0.45 \, \text{dollars per month}$.

2. Account B:

   • Monthly interest = $\frac{I}{t \cdot 12} = \frac{22.50}{27} \approx 0.833 \, \text{dollars per month}$.

Answer: Account B earned more interest in the first month because it earned approximately $0.83, compared to $0.45 for Account A.

Summary:

1. Principal for Account A = $150.
2. Principal for Account B = $400.
3. Account B earned the most interest in the first month.

Questions for Further Practice:

1. How would the principal change if the interest rate for Account A was doubled?
2. If both accounts had the same principal, how much interest would each earn after 1 year?
3. How long would it take for Account B to earn $50 in interest?
4. What is the total interest earned by both accounts after 3 years?
5. How would compound interest affect the total interest for each account?

Tip:

Always convert time into years when using the simple interest formula!