To solve this problem, we will use the formula for compound interest:

A(t) = P(1 + r/n)^(nt)

Where:
A(t) is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money)
r is the annual interest rate (in decimal)
n is the number of times that interest is compounded per year
t is the time the money is invested for in years

Given in the problem:
P = $500
r = 5% = 0.05 (in decimal)
n = 12 (since the interest is compounded monthly)
t = 4 years

Substitute these values into the formula:

A(t) = 500(1 + 0.05/12)^(12*4)

Now, calculate the expression inside the parentheses:

1 + 0.05/12 = 1.00416666667

Then raise this result to the power of 48 (which is 12*4):

(1.00416666667)^48 = 1.22039274854

Finally, multiply this result by the initial principal amount:

500 * 1.22039274854 = $610.20 (rounded to the nearest cent)

So, the answer is $610.20. Therefore, the correct option is C. $610.45.

Question

To solve this problem, we will use the formula for compound interest:

A(t) = P(1 + r/n)^(nt)

Where:
A(t) is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money)
r is the annual interest rate (in decimal)
n is the number of times that interest is compounded per year
t is the time the money is invested for in years

Given in the problem:
P = $500
r = 5% = 0.05 (in decimal)
n = 12 (since the interest is compounded monthly)
t = 4 years

Substitute these values into the formula:

A(t) = 500(1 + 0.05/12)^(12*4)

Now, calculate the expression inside the parentheses:

1 + 0.05/12 = 1.00416666667

Then raise this result to the power of 48 (which is 12*4):

(1.00416666667)^48 = 1.22039274854

Finally, multiply this result by the initial principal amount:

500 * 1.22039274854 = $610.20 (rounded to the nearest cent)

So, the answer is $610.20. Therefore, the correct option is C. $610.45.

Knowee AI · Accepted Answer