Final answer:
A $200 investment at 5% interest compounded monthly for 9 years will be worth approximately $313.05 when rounded to the nearest cent, using the compound interest formula.
Step-by-step explanation:
The question asks how much a $200 investment at 5% interest compounded monthly will be worth after 9 years. To solve this, we use the formula for compound interest: A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
For this question:
- P = $200
- r = 5% or 0.05
- n = 12 (since interest is compounded monthly)
- t = 9 years
Plugging into the formula, we get:
A = 200(1 + 0.05/12)^(12*9)
A = 200(1 + 0.0041666...)^108
A = 200(1.0041666...)^108
A ≈ 200 * 1.565289
A ≈ $313.05
Therefore, after 9 years, the investment will be worth $313.05 when rounded to the nearest cent.