Question

Nicole deposits $30,000 into an account that pays simple interest at a rate of 2% per year.

Chris deposits $30,000 into an account that also pays 2% interest per year. But it is compounded annually.
Find the interest Nicole and Chris earn during each of the first three years.
Then decide who earns more interest for each year.
Assume there are no withdrawals and no additional deposits.
Year
First
Second
Third
Interest Nicole earns
(Simple interest)
$0
$0
$0
Interest Chris earns
(Interest compounded annually)
$
$
$0
Who earns more interest?
Nicole earns more.
Chris earns more.
O They earn the same amount.
Nicole earns more.
Chris earns more.
O They earn the same amount.
O Nicole earns more.
O Chris earns more.
O They earn the same amount.

Answer 1

Step-by-step explanation:To calculate the interest, we need to use the formulas for simple interest and compound interest.

For Nicole, the simple interest formula is , where is the principal amount, is the rate of interest, and is the time in years. Since the interest is simple, it will be the same every year.

For Chris, the compound interest formula is , where is the amount of money accumulated after n years, including interest. The interest earned each year is the difference between the amount for that year and the amount for the previous year.

For Nicole:

Interest for each year =

For Chris:

First year: , so the interest is

Second year: , so the interest is

Third year: , so the interest is

So, the interest earned by Nicole and Chris in the first three years is:

Year | Nicole (Simple Interest) | Chris (Compound Interest)

--- | --- | ---

First | $600 | $600

Second | $600 | $612

Third | $600 | $624.24

Therefore, Nicole and Chris earn the same amount of interest in the first year, but Chris earns more interest in the second and third years due to the effects of compounding.