Question

# You want to open a savings account and you have 3 choices: 1) a saving account...

You want to open a savings account and you have 3 choices: 1) a saving account that pays interest of 7.2% compounded quarterly (In other words, it offers an APR=7.2%, compounded quarterly), 2) a saving account that pays interest of 6.8% compounded monthly, and 3) a saving account that pays interest of 7% continuously compounded?

Which one do you prefer?

First calculating Effective annual rate for all the options.

option 1). APR = 7.2% compounded quarterly,

So, Effective annual rate, EAR = (1 + APR/n)^n - 1

for quarterly compounded, n = 4

=> EAR = (1 + 0.072/4)^4 - 1 = 7.40%

Option 2). APR = 6.8% compounded monthly,

So, Effective annual rate, EAR = (1 + APR/n)^n - 1

for monthly compounded, n = 12

=> EAR = (1 + 0.068/12)^12 - 1 = 7.02%

Option 3). APR = 7% compounded continuously,

For Compounded continuously, EAR = e^APR - 1 = e^0.07 - 1 = 7.25%

Since highest interest rate paying saving account is option 1, it should be preferred.

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