Assume a bank offers an effective annual rate of 5.60%. If compounding is quarterly what is the APR?

Answer 1

To convert the effective annual rate (EAR) to the annual percentage rate (APR) when compounding is quarterly, you can use the following formula:

$$\text{EAR}={(1+\frac{\text{APR}}{n})}^n-1$$

where:

• $n$ is the number of compounding periods per year (in this case, $n=4$ for quarterly compounding).
• $\text{APR}$ is what we want to find.

We are given that the EAR is 5.60%, which we will convert to decimal form: $\text{EAR}=0.056$.

Now we can rearrange the formula to solve for APR:

$$1+\frac{\text{APR}}{4}=(1+\text{EAR}{)}^{1/4}$$

First, rearranging gives us:

$$\frac{\text{APR}}{4}=(1+0.056{)}^{1/4}-1$$

Calculating $(1+0.056{)}^{1/4}$:

$$(1.056{)}^{1/4}\approx 1.013669$$

Now substitute back into the equation:

$$\frac{\text{APR}}{4}=1.013669-1\approx 0.013669$$

Finally, multiplying by 4 to get APR:

$$\text{APR}\approx 0.013669\cdot 4\approx 0.054676$$

Now, convert this to a percentage:

$$\text{APR}\approx 5.47$$

Thus, the annual percentage rate (APR) is approximately 5.47%.

Answer 2

can you give theAPR in 4 decimal?

Answer 3

Sure! From the calculation we previously did, we found:

$$\text{APR}\approx 0.054676$$

To express this as a percentage rounded to four decimal places, we multiply by 100:

$$\text{APR}\approx 0.054676\times 100=5.4676$$

Therefore, the APR, expressed in four decimal places, is approximately 5.4676%.