Question

Adita has two options for how to invest $1,000.

Plan A: Put the $1,000 in an account that pays $100 per year.
Plan B: Put the $1,000 in an account that pays 5 percent interest per year.

Which statement is true?
Plan A will be worth more than plan B after two years.
Plan A will be worth the same amount as plan B after one year.
Plan B will be worth more than plan A after three years.
Plan B will be worth more than plan A after four years.

Answer 1

Compute values:

Plan A (adds $100 each year, no compounding): after t years = 1000 + 100t.
Plan B (5% compound): after t years = 1000*(1.05)^t.

After 1 year:
- A = 1100
- B = 1000(1.05) = 1050

After 2 years:
- A = 1200
- B = 1000(1.05)^2 = 1102.50

After 3 years:
- A = 1300
- B = 1000(1.05)^3 = 1157.63

After 4 years:
- A = 1400
- B = 1000(1.05)^4 = 1215.51

Therefore the true statement is: "Plan A will be worth more than plan B after two years."