The given investment can be handles as an annuity and the value of the
investment is given by the interest rate and the monthly payment.
Responses:
- The financial difference is between investing $200 per month versus $500 per month is $1,048,489.24
- The difference in the amount invested is $108,000
How is the value of an investment involving equal periodic payment calculated?
Given parameter are;
Number of years = 30 years
Rate of return = 12%
Amount invested per month, P = $200 and $500
Future Value, FVA, Â value of monthly investment is given by the formula;
[tex]FVA = \mathbf{P \times \dfrac{\left[(1 + i)^n - 1 \right]}{i}}[/tex]
Therefore, we have;
[tex]FVA_{200} = 200 \times \dfrac{\left[\left(1 + \dfrac{0.12}{12} \right)^{12 \times 30} - 1 \right]}{\dfrac{0.12}{12}} \approx \mathbf{ 698992.83}[/tex]
[tex]FVA_{500} = 500 \times \dfrac{\left[\left(1 + \dfrac{0.12}{12} \right)^{12 \times 30} - 1 \right]}{\dfrac{0.12}{12}} \approx \mathbf{ 1747482.07}[/tex]
[tex]Financial \ difference = \mathbf{FVA_{500} - FVA_{200}}[/tex]
Which gives;
[tex]Financial \ difference = 1747482.07 - 698992.83 = \mathbf{1048489.24}[/tex]
The financial difference is approximately $1,048,489.24
Second part:
The amount invested at $200 per month in 30 years is found as follows;
[tex]Amount \ invested_{(200)}[/tex] = $200 × 12 × 30 = $72,000
[tex]Amount \ invested_{(500)}[/tex] = $500 × 12 × 30 = $180,000
- Difference in amount invested = $180,000 - $72,000 = $108,000
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