Question

Marley is looking into 3 different investment options. He currently makes $57,000 in pre-tax income. He hopes to invest 15% every month while invested in the account.

Option 1: 10% for 10 years

Option 2: 8% for 20 years

Option 3: 7% for 25 years

Criteria for Success: Your response must include the following to receive full credit.

3 pts: The correct Final Value for each investment option.

1 pt: A sentence with the answer explaining what factor impacted the investment the most

1 pt: No spelling or grammar errors

Use the equation: image.png

FV: Future Value

P: Principal (monthly contribution) = _______________

r: monthly interest rate = annual interest rate / 12 = _______________

n: number of contribution periods = ___ months x _________ years = _________

Answer 1

Equation used (future value of an ordinary monthly annuity):
FV = P * [ (1 + r)^n − 1 ] / r

Principal (monthly contribution):
P = 15% of $57,000 per year = 0.15 * 57,000 = $8,550 per year
P (monthly) = 8,550 / 12 = $712.50

Option 1 (10% annual for 10 years)
- r (monthly) = 0.10 / 12 = 0.0083333333
- n = 12 months × 10 years = 120 months
- FV = 712.50 * [ (1 + 0.0083333333)^120 − 1 ] / 0.0083333333
- FV ≈ $145,966

Option 2 (8% annual for 20 years)
- r (monthly) = 0.08 / 12 = 0.0066666667
- n = 12 months × 20 years = 240 months
- FV = 712.50 * [ (1 + 0.0066666667)^240 − 1 ] / 0.0066666667
- FV ≈ $419,500

Option 3 (7% annual for 25 years)
- r (monthly) = 0.07 / 12 = 0.0058333333
- n = 12 months × 25 years = 300 months
- FV = 712.50 * [ (1 + 0.0058333333)^300 − 1 ] / 0.0058333333
- FV ≈ $577,100

Sentence explaining the biggest impact:
The length of time invested (the number of monthly contribution periods) has the largest impact on the final value because compounding over many more periods greatly increases the accumulated amount even when the annual rate is lower.