Final answer:
The balance after 8 years for a $2,000 investment at 7% interest compounded monthly is $3,521.62. The correct option in the final answer is 2) $3,521.62.
Step-by-step explanation:
If $2,000 is invested at 7% compounded monthly, to find the balance after 8 years, we need to use the compound interest formula:
A = P(1 + r/n)nt
Where:
- P = principal amount (the initial amount of money)
- r = annual interest rate (in decimal)
- n = number of times the interest is compounded per year
- t = time the money is invested for (in years)
- A = amount of money accumulated after n years, including interest.
Substituting the given values:
P = $2,000
r = 7% or 0.07 (as a decimal)
n = 12 (since interest is compounded monthly)
t = 8 (the number of years)
Using the compound interest formula, we calculate:
A = 2000(1 + 0.07/12)12*8
After calculating the above expression, we find that the balance A is $3,521.62, which corresponds to option 2.
In conclusion, the correct option in the final answer is 2) $3,521.62.