Final answer:
To decide which investment option is better for Natalia Sanchez, we will calculate the future value of $20,000 compounded daily versus monthly at 4.5% interest rate over 4 years and compare the results.
Step-by-step explanation:
To determine which investment Natalia Sanchez should choose based on annual percentage yield (APY), we need to calculate the compound interest for both scenarios: compounded daily and compounded monthly for $20,000 over 4 years.
Compound interest formula is A = P(1+r/n)^(nt).
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
n = the number of times that interest is compounded per year.
t = the time in years.
For daily compounding:
A = $20,000(1 + 0.045/365)^(365*4).
For monthly compounding:
A = $20,000(1 + 0.045/12)^(12*4).
Calculate both A values and compare to see which one is higher. The one with the higher A value represents the better investment based on APY.