This problem is an example of a Geometric Progression (GP).
A GP usually has the following parameters to describe it:
[tex]\begin{gathered} a=\text{ First term} \\ r=\text{ Common ratio} \end{gathered}[/tex]
From our question, we have the first term to be 50000, and the common ratio is a 3% increase.
We know that if a percentage (p) is given, the actual ratio is given as
[tex]\begin{gathered} r=\frac{p}{100}+1\text{ (For increments)} \\ or \\ r=1-\frac{p}{100}\text{ (for reductions)} \end{gathered}[/tex]
Therefore, the common ratio in our case is
[tex]r=\frac{3}{100}+1=1.03[/tex]
We are to calculate the sum of the GP in the question. The formula for the sum of a GP is given as
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
Since we're calculating the total income up to 10 years, we have
[tex]n=10[/tex]
Therefore, we can calculate the sum to be
[tex]\begin{gathered} S_{10}=\frac{50000(1.03^{10}-1)}{1.03-1} \\ S_{10}=573193.97 \end{gathered}[/tex]
The correct option is OPTION D.
