Review both types of compounded interests. Apply the formulas to different examples with the same annual interest rates. What can you conclude?
See solution.
Practice makes perfect
We can compare both types of compounded interest by using a table.
Annually Compounded Interest
Continuously Compounded interest
A(t) = a(1+r)^t
A(t) = Pe^(rt)
In these formulas A is the amount at time t. P and a represent the initial amounts, and r is the annual interest rate. Both model compounded interest. This is when interest is applied repeatedly over a quantity.
In this model the interest is applied after a specific time period (each year).
In this model the interest is applied continuously, which means that the time period in between each interest application is so small that it is mathematically zero.
It is important to notice that when considering same annual interest rates and same initial amounts, the shorter the time period you have to wait to reapply the interest, the greater the amount will be after a specific time t. This is why continuously compounded interest will always give you a greater amount.
