Final answer:
The account balance in Rob's retirement account after 13 years, given a 5% annual interest rate compounded semiannually, would be approximately $5,987.23.
Step-by-step explanation:
To find out what the account balance will be after 13 years when Rob invests $2,856 in a retirement account with a fixed annual interest rate of 5% compounded 2 times per year, we can use the compound interest formula:
A = P(1 + r/n)(nt)
Where:
- A = the amount of money accumulated after n years, including interest.
- P = the principal amount (the initial amount of money).
- r = the annual interest rate (decimal).
- n = the number of times that interest is compounded per year.
- t = the time the money is invested for in years.
Based on Rob's investment:
- P = $2,856
- r = 0.05 (5% as a decimal)
- n = 2 (since the interest is compounded semiannually)
- t = 13 years
Substitute these values into the formula:
A = 2856(1 + 0.05/2)(2*13)
Calculate the values inside the parentheses and the exponent:
A = 2856(1 + 0.025)26
A = 2856(1.025)26
Using a calculator, we raise 1.025 to the 26th power and multiply the result by $2,856:
A ≈ 2856 * 1.02526
A ≈ 2856 * 2.09659023431
Now multiply 2,856 by approximately 2.0966:
A ≈ 5987.23
After 13 years, the account balance would be approximately $5,987.23.