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?
a) Bank C: 3.70% compounded semi-annually
b) Bank E: 3.65% compounded quarterly
c) Bank D: 3.67% compounded continuously
d) Bank A: 3.75%, compounded annually
e) Bank B: 3.69%, compounded monthly

Answer 1

Answer:

e) Bank B: 3.69%, compounded monthly

Explanation:

Since the interest is compounded for different periods in the options given, find the Effective Annual Interest rate for each Bank. This will be a fair comparison for each option.

Where,

Effective Annual Interest Rate =  ( 1 + i/n) ^ n - 1

Therefore,

Bank C: 3.70% compounded semi-annually

Effective Annual Interest Rate =  ( 1 + i/n) ^ n - 1

                                                  = (1 + 3.70%/2) ^ 2 - 1

                                                  = 7.12 %

Bank E: 3.65% compounded quarterly

Effective Annual Interest Rate =  ( 1 + i/n) ^ n - 1

                                                  = (1 + 3.65%/4) ^ 4 - 1

                                                  = 12.38 %

Bank D: 3.67% compounded continuously

Effective Annual Interest Rate = e ^ i - 1

                                                  = 2.7182818 ^ 3.67% - 1

                                                  = 3.74

Bank A: 3.75%, compounded annually

Effective Annual Interest Rate =  ( 1 + i/n) ^ n - 1

                                                  = (1 + 3.75%/1) ^ 1 - 1

                                                  = 3.75 %

Bank B: 3.69%, compounded monthly

Effective Annual Interest Rate =  ( 1 + i/n) ^ n - 1

                                                  = (1 + 3.69%/12) ^ 12 - 1

                                                  = 23.96 %

Conclusion

Choose the option that is giving the highest Effective Annual Interest Rate. Therefore, choose e) Bank B: 3.69%, compounded monthly.