Final answer:
The question was to calculate the amount in the account after 5 years for $5000 with a semiannual compound interest rate of 2.7%. Using the compound interest formula, the final amount is calculated to be $5718.43. None of the provided options match this calculated value.
Step-by-step explanation:
The student wants to find the final amount in an account after 5 years when $5000 is deposited at an interest rate of 2.7%, compounded semiannually. To calculate this, we can use the formula for compound interest:
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.
By plugging in the values:
- P = $5000
- r = 2.7% or 0.027
- n = 2 (since it is compounded semiannually)
- t = 5 years
The calculation would be:
A = 5000(1 + 0.027/2)^(2*5)
A = 5000(1 + 0.0135)^(10)
A = 5000(1.0135)^(10)
A = 5000(1.143685823588)
A = $5718.43
None of the provided options correctly match the calculated amount. It seems like there might be an error in the options given. The correct answer calculated is $5718.43.