To find the total value of the investment after 8 years with monthly compounding, we can use the formula:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Plugging in the given values, we get:
A = 5000(1 + 0.025/12)^(12*8)
A ≈ $6,105.74
Therefore, the total value of the investment after 8 years is approximately $6,105.74.
So, the correct option is (a) $6,105.74.