Final answer:
After calculating the compounded interest using the appropriate formula, it is determined that $3,000 saved at a 14% annual interest rate compounded yearly will amount to $6,092.57 after six years. None of the provided answers match this correct amount.
Step-by-step explanation:
To determine how much you will have at the end of six years when you save $3,000 at an interest rate of 14 percent per year, compounded annually, you can 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 your question:
- P = $3,000
- r = 14% or 0.14
- n = 1 (since it is compounded annually)
- t = 6 years
Now, we substitute these values into the formula:
A = 3000(1 + 0.14/1)1*6
A = 3000(1 + 0.14)6
A = 3000(1.14)6
A = 3000 * 2.030856
A = $6,092.57 (rounded to two decimal places)
Therefore, none of the options given match the correct answer, as $6,092.57 is not one of the choices provided.