The initial investment of Calvin must be increased by a factor of 115.927 % to equal Marquez's investment at any time. (Correct choice: D)
In this question we must apply the concept of compound interest to derive the initial investment to be done by Calvin. According to the statement, Calvin invests money five years later than Marquez.
To determine the initial investment to be deposited by Calvin such that his investment equals Marquez's investment at any time we resort to the following expression:
[tex]1500\cdot (1+0.03)^{t+5} = C_{C}\cdot (1+0.03)^{t}[/tex] (1)
Then, we simplify the required initial investment:
[tex]C_{C} = 1500\cdot (1+0.03)^{5}[/tex]
[tex]C_{C} = 1738.911[/tex]
And the increase factor is:
[tex]r_{C} = \frac{1738.911}{1500}\times 100\,\%[/tex]
[tex]r_{C} = 115.927\,\%[/tex]
The initial investment of Calvin must be increased by a factor of 115.927 % to equal Marquez's investment at any time. (Correct choice: D) [tex]\blacksquare[/tex]
To learn more on compound interests, we kindly invite to check this verified question: https://brainly.com/question/14295570
