To find the difference between the tow investments we are going to use tow formulas. Simple interest formula for our simple interest investment, and compound interest formula for our compound interest investment.
- Simple interest formula:
where
is the final investment value
is the initial investment
is the interest rate in decimal form
is the time in years
For our problem we know that
, 
, and 
, so lets replace those values in our simple interest formula to find :
Now that we know the final investment value of our simple interest investment, lets use the compound interest formula to find the final investment value of the other one:
- Compound interest formula:
where
is the final investment value
is the initial investment
is the interest rate in decimal form
is the number of times the interest is compounded per year
is the time in years
For our problem we know that, , and . Since we know that the interest is compounded quarterly (each 4 months), it mean that is compounded 
times per year, so 
. Now that we have all the vales, lets replace them in our formula:
now that we know the final amounts of our investments, lets find how much difference is between them:
We can conclude that the difference between invest $5000 in a compound interest investment vs a simple interest investment is $98.95.
- Simple interest formula:
where
For our problem we know that
Now that we know the final investment value of our simple interest investment, lets use the compound interest formula to find the final investment value of the other one:
- Compound interest formula:
where
For our problem we know that
now that we know the final amounts of our investments, lets find how much difference is between them:
We can conclude that the difference between invest $5000 in a compound interest investment vs a simple interest investment is $98.95.