To find the amount in the account after 5 years with interest compounded semiannually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount in the account after t years
- P is the principal amount ($3,000 in this case)
- r is the annual interest rate (6.77% or 0.0677 as a decimal)
- n is the number of times the interest is compounded per year (semiannually means twice a year)
- t is the number of years (5 years in this case)
Plugging in the values:
A = 3000(1 + 0.0677/2)^(2*5)
A = 3000(1 + 0.03385)^10
A = 3000(1.03385)^10
A = 3000(1.419398)
A ≈ $4258.19
Therefore, the amount in the account after 5 years with interest compounded semiannually would be approximately $4258.19.
