Question

Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)

Answer 1

To determine which option would help to increase Belinda's investment value by the greatest amount in 20 years, we need to calculate the value of each option after 20 years and compare them.

Option 1:
Initial investment = $50,000
Annual interest rate = 5%
Compounded semi-annually
Time period = 20 years

Using the formula for compound interest, we can calculate the value of the investment after 20 years:

A = P(1 + r/n)^(nt)
A = 50,000(1 + 0.05/2)^(2*20)
A = $132,676.19

Option 2:
Initial investment = $50,000
Annual interest rate = 5.5%
Compounded annually
Time period = 20 years

Using the same formula, we can calculate the value of the investment after 20 years:

A = P(1 + r/n)^(nt)
A = 50,000(1 + 0.055/1)^(1*20)
A = $144,456.38

Therefore, after 20 years, the value of Belinda's investment using option 2 would be $144,456.38, while the value of her investment using option 1 would be $132,676.19. This means that there would be a significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1. The difference in investment value would be $11,780.19, which is the amount by which option 2 exceeds option 1. Therefore, option 2 would be the better choice for Belinda if she wants to increase her investment value by the greatest amount in 20 years.