Caleb deposits $13,500 into an account that earns 2.5% interest compounded monthly. How much does Kaya have in the account after 7 years 6 months? O $16,280.93 O $16.978.90 O $16,552.55 O $16,031.25

1. Use the formula for compound interest:
A = P \left(1 + \frac{r}{n}\right)^{nt}

2. Substitute the given values into the formula:
- Principal ( P ) = 13,500
- Annual interest rate ( r ) = 2.5% = 0.025
- Number of times interest is compounded per year ( n ) = 12
- Time in years ( t ) = 7.5 years

Therefore:
A = 13500 \left(1 + \frac{0.025}{12}\right)^{12 \cdot 7.5}

3. Calculate the monthly interest rate:
1 + \frac{0.025}{12} = 1 + 0.002083 = 1.002083

4. Calculate the exponent:
12 \cdot 7.5 = 90

5. Raise 1.002083 to the power of 90:
1.002083^{90} \approx 1.206738

6. Multiply by the principal:
A \approx 13500 \times 1.206738 = 16,280.93

Therefore, the amount in the account after 7 years and 6 months is 16,280.93 .