Final answer:
In order to find out how much money Rachel should invest today in a fund that earns interest at 3.24% compounded quarterly, we can use the compound interest formula. Plugging in the given values, Rachel should invest approximately $4,659.72 today.
Step-by-step explanation:
In order to determine the present investment needed for Rachel to receive $6,000 every six months for the next five years, the compound interest formula is applied.
The formula, A = P(1 + r/n)^(nt), represents the future value of the investment, where P is the principal amount, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
In Rachel's scenario, with quarterly compounding over 5 years (10 compounding periods), and an annual interest rate of 3.24% (0.0324 as a decimal), the formula is configured as $6,000 = P(1 + 0.0324/4)^(4*5).
Solving for P yields approximately $4,659.72.
Therefore, Rachel should invest around $4,659.72 today to ensure the receipt of $6,000 every six months for the next five years, factoring in the specified compounding frequency and interest rate.