A. Quarterly Compounding:
First, we need to calculate the quarterly interest rate, which is 5%/4 = 1.25%.
After the first quarter, the balance becomes:
3100 + (1.25% * 3100) = $3138.75
After the second quarter, the balance becomes:
3138.75 + (1.25% * 3138.75) = $3177.91
After the third quarter, the balance becomes:
3177.91 + (1.25% * 3177.91) = $3217.43
After the fourth quarter, the balance becomes:
3217.43 + (1.25% * 3217.43) = $3257.31
Therefore, the balance after 2 years with quarterly compounding is $3257.31.
B. Monthly Compounding:
First, we need to calculate the monthly interest rate, which is 5%/12 = 0.4167%.
After the first month, the balance becomes:
3100 + (0.4167% * 3100) = $3113.25
After the second month, the balance becomes:
3113.25 + (0.4167% * 3113.25) = $3126.53
After the twenty-fourth month, the balance becomes:
3335.08 + (0.4167% * 3335.08) = $3461.85
Therefore, the balance after 2 years with monthly compounding is $3461.85.
C. Continuous Compounding:
The formula for continuous compounding is:
A = Pe^(rt)
where A is the balance after time t, P is the principal, r is the interest rate, and e is the mathematical constant e (approximately equal to 2.71828).
Plugging in the values, we get:
A = 3100 * e^(0.05 * 2) = $3398.98
Therefore, the balance after 2 years with continuous compounding is $3398.98.