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.
