Question

Savings account A and savings account B both offer APRs of 4%, but savings account A compounds interest semiannually, while savings account B compounds interest quarterly. Which savings account offers the higher APY?

Answer 1

Saving account B because it has more compounding periods per year
Quarterly means 4 times per year
Semiannual means 2 times per year

Answer 2

Answer:

Savings account B offers the higher APY.

Step-by-step explanation:

Let the principal amount be 1000 and time be 1 year.

We are told that savings account A and savings account B both offer APR's of 4%, but savings account A compounds interest semiannually, while savings account B compounds interest quarterly.

We will use compound interest formula to answer our given problem.

$A=P(1+\frac{r}{n})^{nT}$, where,

A= Final amount after T years.

P= Principal amount.

r= Annual interest rate in decimal form.

n= Number of times interest in compounding per year.

T= Time in years.

Let us find amount that savings account A will give after 1 year.

Semiannually means twice a year, so n will be 2.

$4\%=\frac{4}{100}=0.04$

$A=1000(1+\frac{0.04}{2})^{2\cdot 1}$

$A=1000(1+0.02)^{2}$

$A=1000(1.02)^{2}$  

$A=1000\times 1.0404$

$A= 1040.4$

Therefore, amount in savings account A after 1 year will be $1040.4.

Now let us figure out amount that savings account B will give after 1 year.

Compounded quarterly means 4 times a year, so n will be 4.

$A=1000(1+\frac{0.04}{4})^{4\cdot 1}$

$A=1000(1+0.01)^{4}$

$A=1000(1.01)^{4}$

$A=1000\times 1.04060401$  

$A=1040.60401\approx 1040.6$      

Therefore, amount in savings account B after 1 year will be $1040.6.

We can see that amount is savings account B is more that account A. Therefore, savings account B offers the highest APY as account B has more compounding periods than account A .