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

Savings account B offers the higher APY.

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+(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\%=(4)/(100)=0.04`

`A=1000(1+(0.04)/(2))^(2\cdot 1)`

`A=1000(1+0.02)^(2)`

`A=1000(1.02)^(2)`

`A=1000* 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+(0.04)/(4))^(4\cdot 1)`

`A=1000(1+0.01)^(4)`

`A=1000(1.01)^(4)`

`A=1000* 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 .