Ariel deposits $5000 in an account that earns simple interest at an annual rate of 3%. Travis deposits $5000 in an account that earns compound interest at annual rate of 3%
To calculate the interest earned by Ariel and Travis, we need to understand the difference between simple interest and compound interest.
Simple interest is calculated based on the initial amount or principal, whereas compound interest is calculated based on the initial amount as well as accumulated interest from previous periods.
For Ariel's account with simple interest at an annual rate of 3%, we can calculate the interest earned using the following formula:
Simple Interest = Principal x Interest Rate
In this case, Ariel's principal amount is $5000 and the interest rate is 3%. Therefore, the interest earned by Ariel's account can be calculated as:
Interest = $5000 x 0.03 = $150
Travis, on the other hand, has a compound interest account. Compound interest is calculated using the following formula:
Compound Interest = Principal x (1 + Interest Rate)^Time - Principal
In this case, Travis also has a principal amount of $5000 and an interest rate of 3%. However, we need to know the time period to calculate the overall interest earned.
Let's assume the time period is 1 year. Using the formula, the compound interest for Travis' account would be:
Compound Interest = $5000 x (1 + 0.03)^1 - $5000
= $5000 x (1.03) - $5000
= $5150 - $5000
= $150
So, in this scenario, both Ariel and Travis would earn the same interest of $150. The only difference is that Ariel's interest is simple interest, while Travis earns compound interest.