Question

You plan to deposit $5,500 into a savings account. There are five great banks in your town offering terrific interest rates. If your goal is to earn the greatest amount of interest, which bank should you choose?

Bank DEF: 3.70%, compounded monthly

Bank ABC: 3.74%, compounded annually

Bank HIJ: 3.71% compounded semi-annually

Bank XYZ; 3.64% compounded quarterly

Bank KLM: 3.66% compounded continuously

Answer 1

Deposit (P) =

$    5,500

Time Period (assume)

1 Year

Formula for Future Value; (Discrete Compounding)  Amount = P(1+(i/n))ⁿ, where n= frequency of Compounding

(Continous Compounding)  Amount = P e^rt, where t= time Period; r = Rate of Interest

Bank	Interest Rate	Compounding Frequency	Computation of Amount = P(1+i)^n		Amount at the end of the year
DEF	3.70%	Monthly	Amount = $ 5,500 (1+(0.037/12))^(1*12)	=$ 5,500*1.0376	5706.987
ABC	3.74%	Annually	Amount = $ 5,500 (1+0.0374)^1	=$ 5,500*1.0374	5705.7
HIJ	3.71%	Semi Annually	Amount = $ 5,500 (1+(0.0371/2))^(1*2)	=$ 5,500*1.03744	5705.943
XYZ	3.64%	Quarterly	Amount = $ 5,500 (1+(0.0364/4))^(1*4)	=$ 5,500*1.0369	5702.949
KLM	3.66%	Continously	Amount = $ 5,500 *e^(0.0366*1)	=$ 5,500*1.03728	5705.029

As Amount is higher in DEF Bank, it is better to invest in DEF Bank.