Example functions: y_1= 1000(1.12)^t and y_2= 1000(1.01)^(12t) Better option: y_2= 1000(1.01)^(12t) Explanation: See solution.
Practice makes perfect
Let's recall the form of an exponential function modeling compound interest.
y= P(1+ r/n)^(nt)In this form y is the balance of the account, P is the principal or initial amount, r is the annual interest rate (in decimal form), t is the time in years, and n the number of times interest is compounded per year. Below we can find a table with the descriptions and the corresponding functions for two different accounts.
Note that both accounts offer the same annual interest rate. Then, which is the best option? Well, there is a big difference. Notice that Account 2 composes the interest monthly, while Account 1 does this once a year.
We can see the impact of this effect in the graph below.
As we can see, the amount in Account 2 eventually overcomes the amount in Account 1. This is because the interest is compounded each month, and then the next month generates interest over a quantity already possessing an interest benefit. This is why that account's money grows faster, and therefore, is the best option.
