Final answer:
The balance after 6 years with a principal of $5,000 earning 7% compounded annually is $7,612.26. The compound interest formula A = P(1 + r/n)^(nt) is used to calculate the final amount in the account.
Step-by-step explanation:
To find the balance in the account after 6 years with a principal of $5,000 earning 7% compounded annually, we need to use the formula for compound interest. The formula is:
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 or borrowed for, in years.
In this case, we have:
- P = $5,000
- r = 7% or 0.07
- n = 1 (since interest is compounded annually)
- t = 6 years
Let's calculate the balance after 6 years:
A = $5,000(1 + 0.07/1)^(1*6)
A = $5,000(1 + 0.07)^6
A = $5,000(1.07)^6
A = $5,000 * 1.5
After calculating the power of 1.076, we multiply by the principal, $5,000, to find the final balance. Don't forget to round to the nearest cent as requested.
A = $7,612.26
Therefore, the balance after 6 years will be $7,612.26.