Final answer:
Christine needs to invest $56,839, rounding to the nearest dollar, to reach her goal of $79,400 in 15 years with an annual interest rate of 2.24% compounded daily.
Step-by-step explanation:
To calculate how much Christine needs to invest now to have $79,400 after 15 years at an interest rate of 2.24% compounded daily, we use the formula for compound interest: P = A / (1 + r/n)^(nt). Here, 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, and t is the time the money is invested for in years.
Christine wants the future value A to be $79,400, r is 2.24% or 0.0224 in decimal form, n is 365 as the interest is compounded daily, and t is 15 years. Using these values, the formula becomes: P = 79400 / (1 + 0.0224/365)^(365*15).
Now we calculate the initial investment P:
P = 79400 / (1 + 0.0000613698630137)^(5475)P = 79400 / (1.0000613698630137)^(5475)P = 79400 / 1.3975865361557P = $56839.06
Therefore, Christine needs to invest $56,839, rounded to the nearest dollar, to have $79,400 after 15 years with daily compounding at a rate of 2.24%.