annas bank gives her a loan with a stated interest rate of 10.22%. how much greater will annas effective…

Explanation:

Step1: Recall the effective - interest rate formula

The formula for the effective - interest rate $r_{eff}$ is $r_{eff}=(1 + \frac{r}{n})^{n}-1$, where $r$ is the stated annual interest rate and $n$ is the number of compounding periods per year. The stated interest rate $r = 0.1022$.

Step2: Calculate the effective - interest rate for monthly compounding

For monthly compounding, $n = 12$. Then $r_{eff1}=(1+\frac{0.1022}{12})^{12}-1$. [ \begin{align*} r_{eff1}&=(1 + 0.0085167)^{12}-1\ &\approx1.10717 - 1\ &=0.10717 \end{align*} ]

Step3: Calculate the effective - interest rate for daily compounding

For daily compounding, assume 365 days in a year, so $n = 365$. Then $r_{eff2}=(1+\frac{0.1022}{365})^{365}-1$. [ \begin{align*} r_{eff2}&=(1+\frac{0.1022}{365})^{365}-1\ &=(1 + 0.00028)^{365}-1\ &\approx1.107633-1\ &=0.107633 \end{align*} ]

Step4: Find the difference

The difference $\Delta r=r_{eff2}-r_{eff1}=0.107633 - 0.10717=0.000463$, which is $0.0463$ percentage points.

Answer:

d. 0.0463 percentage points