Question

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?

Answer 1

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:

`A=P(1+(r)/(n))^(nt)`

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:

`A=P(1+rt)`

And compound continuosly:

`A=\text{Pe\textasciicircum{}rt}`

Let's calculate the final amount for each case

Bank A

`A=20000(1+(0.0425)/(12))^(12\cdot5)=24726.038`

Bank B

`A=20000(1+(0.06)/(2))^(2\cdot5)=26878.328`

Bank C

`A=20000(1+0.055\cdot5)=25500`

Bank D

`A=20000e^(0.04\cdot5)=24428.055`

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