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
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.
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