Answer:
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.