Describe the difference between simple interest and compound interest. Why does it make sense that the interest rate r is divided by n in the compound interest formula?
Discussion – Simple Interest and Compound Interest
Simple interest refers to interest that is only paid on the principal amount of a loan. The principle is the original amount borrowed, and it does not include any interest that has been accrued (Billstein, Libeskind & Lott, 2013). For example, if you take out a loan for $100 and the interest rate is 20%, you would owe $120 at the end of the year. The extra $20 is the interest that you have accrued. Besides, the 20% interest is only applied to the original $100 principal- not the $20 interest that was earned during the year. The formula for simple interest is:
I=P(1+rt)
I= the total interest accrued
P= the original principal amount
r= the interest rate (as a decimal)
t= the time in years that the loan is taken out for
Compound interest, on the other hand, is when interest is earned not only on the original principal amount but also on the accumulated interest of previous periods (Billstein, Libeskind & Lott, 2013). In other words, compound interest is “interest on interest.” To continue with our example from before, if you take out a loan for $100 with a 20% annual interest rate, you would owe $120 at the end of the first year. In the second year, 20% interest would be applied not only to the original $100 principal but also to the $20 in interest that was earned during the first year. This means that you would owe a total of $144 at the end of the second year.
The formula for compound interest is:
A=P(1+r/n)^nt
A= the total amount of money owed after n years
P= the original principal amount
l= the number of compounding periods per year
r= the interest rate (as a decimal)
n= the number of years that the loan is taken
t= the number of compounding periods
As you can see, the main difference between simple and compound interest is that with compound interest, you earn interest not only on your original principal amount but also on the accumulated interest of previous periods.
References
Billstein, R., Libeskind, S., & Lott, J. (2013). Problem Solving Approach to Mathematics for Elementary School Teachers, A: Pearson New International Edition PDF eBook. Pearson Higher Ed.