To determine which investment is the best deal for Luisa Hernandez's $20,000 investment over 4 years, we need to compare the two options: daily compounding at 3.5% and monthly compounding at 3.75%.
For the daily compounding option at 3.5%, we can calculate the final amount using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the initial principal ($20,000)
r = the annual interest rate (3.5% or 0.035)
n = the number of times interest is compounded per year (365 for daily compounding)
t = the number of years (4)
Plugging in the values, we get:
A = 20000(1 + 0.035/365)^(365*4)
For the monthly compounding option at 3.75%, we use the same formula with a few adjustments:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the initial principal ($20,000)
r = the annual interest rate (3.75% or 0.0375)
n = the number of times interest is compounded per year (12 for monthly compounding)
t = the number of years (4)
Plugging in the values, we get:
A = 20000(1 + 0.0375/12)^(12*4)
To determine which investment option is better, we need to compare the final amounts (A) for both options. The higher the final amount, the better the deal.
Now, calculating the final amounts for both options, we find:
For daily compounding at 3.5%: A ≈ $23,032.68
For monthly compounding at 3.75%: A ≈ $23,293.83
Comparing the final amounts, we can see that the investment with monthly compounding at 3.75% is the better deal, as it provides a higher return of approximately $23,293.83 compared to the daily compounding option's approximate return of $23,032.68 over the 4-year period.
