Final answer:
The future value of an $800 investment at 10% interest after 6 years depends on the compounding frequency: annually, it's $1,420.64; quarterly, it's $1,472.31; and monthly, it's $1,491.58. Subtract the original investment to calculate the interest earned.
Step-by-step explanation:
If $800 is invested at 10% compounded annually, quarterly, and monthly, the future value after 6 years can be calculated using the compound interest formula A = P(1 + r/n)^(nt), where:
- 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 or borrowed for, in years
- A is the amount of money accumulated after n years, including interest.
Compounded Annually
For annual compounding (n = 1):
A = 800(1 + 0.10/1)^(1*6) = 800(1 + 0.10)^6
A = $1,420.64
Compounded Quarterly
For quarterly compounding (n = 4):
A = 800(1 + 0.10/4)^(4*6)
A = $1,472.31
Compounded Monthly
For monthly compounding (n = 12):
A = 800(1 + 0.10/12)^(12*6)
A = $1,491.58
To determine the interest earned, subtract the principal ($800) from the accumulated amount (A).