Final answer:
The future value of $200 invested at a 4% interest rate compounded monthly after 8 years is approximately $276.84, rounded to the nearest cent.
Step-by-step explanation:
To calculate the future value of $200 invested at 4% interest compounded monthly for 8 years, we need to use the compound interest formula:
Future Value = P (1 + r/n)(nt)
Where:
P = principal amount (initial investment)
r = annual interest rate (decimal)
n = number of times the interest is compounded per year
t = number of years
Substituting the given values into the formula:
P = $200
r = 0.04 (4% expressed as a decimal)
n = 12 (monthly compounding)
t = 8 years
Future Value = 200 (1 + 0.04/12)(12*8)
Calculating the future value:
Future Value = 200 (1 + 0.0033333)96 ≈ 200 (1.0033333)96 ≈ 200 * 1.38422 ≈ $276.84
The future value of the $200 invested at a 4% interest rate, compounded monthly, after 8 years would be approximately $276.84, rounded to the nearest cent.