Final answer:
Using the compound interest formula for an investment compounded quarterly, Michael's $2000 annuity investment at an interest rate of 4% for 5 years will grow to $2433.31.
Step-by-step explanation:
To determine the value of Michael's annuity investment after 5 years, we need to apply the formula for compound interest. Since the interest is compounded quarterly, we will use the formula A = P(1 + r/n)nt, where:
P is the principal amount ($2000).
- r is the annual interest rate (4%, or 0.04).
- n is the number of times the interest is compounded per year (4, for quarterly).
- t is the time the money is invested for (5 years).
Plugging the values into the formula, we get:
A = 2000(1 + 0.04/4)4*5 = 2000(1 + 0.01)20 = 2000 * 1.0120
After calculating the above, we find that the value of the investment after 5 years is $2433.31, which matches option c.