Which is better: An account that pays 8% annual interest compunded quarterly or an account that pays 7.95% annual interest compounded continuously?

Question

Which is better: An account that pays 8% annual interest compounded quartely or an account that pays 7.95% annual interest compounded continuously? Give an algebra analysis to support your answer. (Prove why your choice is better)

Answer 1

Hi there! We are going to use two different equations for this. For the quarterly compounded interest we will use:

A = P[1+(r/n)\^(nt) Where P is our principal (amount invested), r is our interest rate (in decimal form), n is the number of times we compound annually, and t is time in years.

For the continuous compound we will use:

A = Pe^(rt) Again P is principal, r is interest rate, and t is time. The e stands for Euler's number, so when you solve your equation look for the "e" button on your calculator..

Now, let's say we will invest $100 for 10 years. We will plug 1 in for P, 1 in for t, and in the first equation we will plug .08 in for r while we plug .0795 in for r in the second equation. Also, for our n in equation one, we will use 4 since we are compounding quarterly and there are 4 quarters in a year:

A = 100[ 1 + (.08/4)]^(4*10) A = 100*e^(.0795*10)

Now we can plug this into our calculator and get the following answers:

A = $220.80 A = $221.44

As you can see, even though the interest rate with the continuous compound equation is lower, we end up with more money over the course of 10 years. So, in this case, it would be better to go with the continuous compounding.

I hope this explanation was thorough and helped answer all of your questions. If you have any additional questions please don't hesitate to reach out! Learn on :)