If $1000 is invested in an account that earns 11.75%, compounded annually, what will the account balance be after 12 years?
1000(1+0.1175)^12 = 3792.90
To find the account balance after 12 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final account balance
P = the initial principal amount ($1000 in this case)
r = the annual interest rate (11.75%, which needs to be converted to decimal form: 0.1175)
n = the number of compounding periods per year (since it's compounded annually, n = 1)
t = the number of years (12 in this case)
Substituting the values into the formula:
A = 1000(1 + 0.1175/1)^(1*12)
A = 1000(1 + 0.1175)^12
A = 1000(1.1175)^12
Now we can calculate this using a calculator or a math software:
A ≈ 3221.95
Therefore, the account balance after 12 years will be approximately $3221.95.