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You have $20,000 that you want to deposit into a savings account. You have four options to choose from, Bank A offers 4.25% compounded monthly, (Ex 2) Bank B offers 6% compounded Semi Annually, (Ex 2) Bank C offers a simple interest account with a 5.5% rate, (Chapter 8.3) Bank D offers a rate of 4% compounded continuously. (Ex 3) How much money will you have in each account if you let the money sit for 5 years? Which is the best choice?

Sagot :

Problem

You have $20,000 that you want to deposit into a savings account.

You have four options to choose from, Bank A offers 4.25% compounded monthly, (Ex 2) Bank B offers 6% compounded Semi Annually, (Ex 2) Bank C offers a simple interest account with a 5.5% rate, (Chapter 8.3) Bank D offers a rate of 4% compounded continuously. (Ex 3) How much money will you have in each account if you let the money sit for 5 years? Which is the best choice?​

Solution

For this case we need to take in count the compound interest formula given by:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where P= 20000, r= interest rate in fraction and n= number of times that the rate is compounded in a year, t= 5 years and A is the future value

And the simple interest formula:

[tex]A=P(1+rt)[/tex]

And compound continuosly:

[tex]A=\text{Pe\textasciicircum{}rt}[/tex]

Let's calculate the final amount for each case

Bank A

[tex]A=20000(1+\frac{0.0425}{12})^{12\cdot5}=24726.038[/tex]

Bank B

[tex]A=20000(1+\frac{0.06}{2})^{2\cdot5}=26878.328[/tex]

Bank C

[tex]A=20000(1+0.055\cdot5)=25500[/tex]

Bank D

[tex]A=20000e^{0.04\cdot5}=24428.055[/tex]

And the best choice for this case seems to be Bank B since we will have more money at the end of the 5 year

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