Final answer:
To find the annual interest rate that would give Antonia the same amount of interest as a 5% monthly interest rate, we can use the compound interest formula. The annual interest rate would be approximately 64.4%.
Step-by-step explanation:
To find the annual interest rate that would give Antonia the same amount of interest as a 5% monthly interest rate, we need to consider the compound interest formula. The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where A is the future amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, we can set up the equation:
A = P(1 + 0.05/12)^(12*1)
Since we want to find the annual interest rate r, we can rearrange the formula:
r = (A/P)^(1/t) - 1
Plugging in the values, we get:
r = (1 + 0.05/12)^(12*1) - 1
Simplifying the calculation, we find that the annual interest rate that would give Antonia the same amount of interest is approximately 64.4%.