This question is a case of what is known as the Compounding Problem and it's solution will require the compounding formula, which is:
[tex] F=P(r)^n [/tex]
Where [tex] F [/tex] is the Future Value of the investment
[tex] P [/tex] is the opening amount
[tex] r [/tex] is the common ratio
[tex] n [/tex] is the number of months
In such questions our main aim should be to find the common ratio, [tex] r [/tex] and it can be easily found once we realize that there is a relationship between the three terms which have been given to us and that is the ratio of the next term to the present term is always a constant.
Let us check. Take the first second term and divide it by the first as follows:
[tex] \frac{1545}{1500} =1.03 [/tex]
As we can see the ratio is 1.03
Again, the ratio of the third term to the second is:
[tex] \frac{1591.35}{1545}=1.03 [/tex]
Again the ratio is 1.03. Thus, we call it the Common Ratio.
Now, that the common ration has been successfully determined, all that we need to do to find the balance in 2 years is to use the aforementioned formula and to keep in mind the fact that in 2 years, the number of months, or n, is 24.
Now that all the required parameters are known, let us apply the formula
[tex] F=1500(1.03)^{24} \approx3049.2 [/tex]
Thus, at the end of 2 years, the balance in Jameson's account will be $3049.2
