Elizabeth deposits a total of $750 into her savings account each year. The account earns 2% interest compounded annually. The table below shows details for the first three years the account was open. How much interest was earned the 4th year?

Elizabeth earns $ 154.86 due to interests from the beginning to the fourth year and $ 62.75 due to interest only in the fourth year.

Step-by-step explanation:

Elizabeth deposits each year the same amount, which becomes greater due to composite interest. From statement, we notice the following formulas of recurrence:

Initial amount ()

(1)

First year ()

(2)

Second year ()

(3)

Third year ()

(4)

Fourth year ()

(5)

Where:

- Initial amount of Elizabeth's account, measured in US dollars.

- Interest rate ratio, dimensionless.

If we know that and , then the interest earned by Elizabeth in the 4th year is:

First year

(6)

Second year

(7)

Third year

(8)

Fourth year

(9)

The money gained due to interest is determined by the following sum, that is:

Elizabeth earns $ 154.86 due to interests from the beginning to the fourth year and $ 62.75 due to interest only in the fourth year.

21

jk it's 20

step-by-step explanation: