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 = $200
r = 4% or 0.04 (in decimal)
n = 12 (since the interest is compounded monthly)
t = 8 years

Substitute these values into the formula:

A(t) = 200(1 + 0.04/12)^(12*8)

Now, calculate the expression inside the parentheses:

1 + 0.04/12 = 1.003333...

Then raise this result to the power of 96 (12*8):

(1.003333...)^96 = 1.368485...

Finally, multiply this result by the initial principal amount:

200 * 1.368485... = $273.70

So, the amount of $200 invested at 4% interest compounded monthly would be worth approximately $273.70 after 8 years. Therefore, the closest answer is C. $273.71.

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 = $200
r = 4% or 0.04 (in decimal)
n = 12 (since the interest is compounded monthly)
t = 8 years

Substitute these values into the formula:

A(t) = 200(1 + 0.04/12)^(12*8)

Now, calculate the expression inside the parentheses:

1 + 0.04/12 = 1.003333...

Then raise this result to the power of 96 (12*8):

(1.003333...)^96 = 1.368485...

Finally, multiply this result by the initial principal amount:

200 * 1.368485... = $273.70

So, the amount of $200 invested at 4% interest compounded monthly would be worth approximately $273.70 after 8 years. Therefore, the closest answer is C. $273.71.

Knowee AI · Accepted Answer