Find the effective annual interest rate for the given nominal annual interest rate. Round your answers to the nearest
0.01%.
-4.1% compounded hourly (assume 365 days per year)

Question

Quizplus · Accepted Answer

The effective annual interest rate can be calculated using the formula: $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount after time $t$, $P$ is the principal amount (initial investment), $r$ is the annual nominal interest rate (as a decimal), $n$ is the number of compounding periods per year, and $t$ is the time the money is invested for in years. To find the effective annual rate (EAR), we set $P = 1$ and $t = 1$, and solve for $A$, then calculate $EAR = (A - 1) \times 100\% $.Given: $r = 4.1\% = 0.041$, $n = 24 \times 365$ (since it's compounded hourly and there are 24 hours in a day), and $t = 1$ year.$A = (1 + \frac{0.041}{24 \times 365})^{24 \times 365}$Calculating this gives an $A$ value slightly greater than 1.0419, and converting this to a percentage and subtracting 100% gives an EAR slightly above 4.18%, which when rounded to the nearest 0.01% is 4.19%.

Find the Effective Annual Interest Rate for the Given Nominal