Final answer:
The student's question involves solving for the initial deposit needed to reach a future amount through compound interest that's compounded fortnightly at a 10% annual rate.
Step-by-step explanation:
The question pertains to the concept of compound interest, specifically calculating the initial deposit required for it to grow to a certain amount given a fixed interest rate compounded fortnightly. To find out the amount needed to be deposited (the principal), we would use the compound interest formula:
A = P(1+r/n)^(nt)
Where:
A 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 (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for in years.
By rearranging the formula to solve for P, and substituting the given values (A = $24,319, r = 10% or 0.10, n = 26 for fortnightly compounding, and t to be determined), we can calculate the initial deposit required.