Question

Find the APY corresponding to the following nominal rate. 2​% compounded quarterly The APY is ____​%. ​(Type an integer or a decimal. Round to the nearest hundredth as​ needed.)

Answer 1

Answer:

2.02%.

Step-by-step explanation:

We are asked to find the Annual Percentage Yield (APY) for the nominal rate of 2% compounded quarterly.

We will use APY formula to solve our given problem.

$APY=(1+\frac{r}{n})^n-1$, where,

r = Stated annual interest rate in decimal form,

n = Number of times interest is compounded per year.

$2\%=\frac{2}{100}=0.02$

Compounded quarterly means that the value of n is 4.

$APY=(1+\frac{0.02}{4})^4-1$

$APY=(1+0.005)^4-1$

$APY=(1.005)^4-1$

$APY=1.020150500625-1$

$APY=0.020150500625$

Let us convert 0.020150500625 to percent as:

$0.020150500625\times 100\%=2.0150500625\%\approx 2.02\%$

Therefore, the required APY would be 2.02%.

$APY\approx 0.020150500625$

Answer 2

Annual percentage yield is the annual effective rate. The Annual percentage yield is 2.02%.

What is the Annual percentage yield?

The annual percentage yield is the annual effective rate, therefore, it is the rate that will be charged or the rate at which the principal amount will grow during the entire year.

$APY = (1+\dfrac{r}{n})^n-1$

As it is given that the rate of interest is 2% compounded quarterly, therefore, the Annual percentage yield can be written as,

$APY = (1+\dfrac{r}{n})^n-1$

Now, since the rate of interest is 2%, therefore, r = 0.02, while the interest is compounding quarterly, so = n =4,

$APY = (1+\dfrac{0.02}{4})^4-1\\\\APY = 0.020150\\\\APY = 2.015\% \approx 2.02\%$

Hence, the Annual percentage yield is 2.02%.

Learn more about Annual Percentage Yield:

https://brainly.com/question/8151146