Final answer:
The accumulated value of $750 invested at an 8% annual compound rate for 6 years will be approximately $1,814.08, calculated using the compound interest formula. This demonstrates the power of compound interest over time.
Step-by-step explanation:
Finding the Accumulated Value with Compound Interest
To find the accumulated value of $750 invested at a compound rate of 8% per annum for 6 years with annual compounding, we use the compound interest formula:
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 particular question:
- P = $750
- r = 8% or 0.08
- n = 1 (since interest is compounded annually)
- t = 6 years
Now, plugging these values into the formula:
A = 750(1 + 0.08/1)1×6
A = 750(1.08)6
A ≈ $1,814.08
The accumulated value after 6 years will be approximately $1,814.08, which is option d).
Notice how compound interest can lead to a significant increase in the investment compared to simple interest. Over longer periods and with larger sums of money, the benefits of compounding become even more pronounced, as seen in the examples provided.