Find the balance in the account: $2,000 principal, earning 7% compounding semi-annually, after 25 years.
To find the balance in the account after 25 years, 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 (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
In this case:
P = $2,000
r = 0.07 (7%)
n = 2 (compounded semi-annually)
t = 25 years
A = 2000(1 + 0.07/2)^(2*25)
A = 2000(1 + 0.035)^50
A = 2000(1.035)^50
A = 2000(3.869683)
A = $7739.37
The balance in the account after 25 years would be $7,739.37.