Question

You have $2,500 to deposit into a savings account. The five banks in your area offer the following rates. In which bank should you deposit your savings?

Bank B: 3.69%, compounded monthly

Bank A: 3.75%, compounded annually

Bank E; 3.65% compounded quarterly

Bank D: 3.67% compounded continuously

Bank C: 3.70% compounded semi-annually

Answer 1

From the given rates, we must first calculated EAR i.e. compounded annually rates to compare all the option.

Bank B, APR = 3.69% compounded monthly

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

here n = 12 months in a year

=> EAR = (1+ 0.0369/12)^12 - 1 = 3.7531%

Bank A, APR = 3.75% compounded annually,

So, EAR = 3.75%

Bank E, APR = 3.65% compounded quarterly,

n = 4 quarters in a year

=> EAR = (1 + 0.0365/4)^4 - 1 = 3.7003%

Bank D APR = 3.67% compounded continuously,

For compounded continuously, EAR = e^APR - 1 = e^0.0367 - 1 = 3.7382%

Bank C, APR = 3.70% compounded semiannually,

nn = 2 semiannual in a year

=> EAR = (1 + 0.037/2)^2 - 1 = 3.7342%

Since highest interest rate in EAR term is from Bank B, This bank should be selected.