If $540 is invested in an account that earns 19.75%, compounded annually, what will the account balance be after 12 years? (Round your answer to the nearest cent.)
=
P = Po(1+r)^n.
r = 19.75% / 100% = 0.1975 = APR exprssed as a decimal.
n = 1Comp/yr * 12yrs. = 12 Compounding
periods.
P = 540(1.1975)^12 = $4695.70
To calculate the account balance after 12 years with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = final account balance
P = principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years
Let's plug in the given values into the formula:
P = $540
r = 19.75% = 0.1975 (as a decimal)
n = 1 (compounded annually)
t = 12
A = 540(1 + 0.1975/1)^(1*12)
Now, we can simplify the equation by performing the necessary calculations:
A = 540(1 + 0.1975)^12
Next, calculate the value inside the parentheses:
A = 540(1.1975)^12
Using a calculator, raise 1.1975 to the power of 12:
A ≈ 540(1.481151)
Multiply the two values together:
A ≈ $799.02
Therefore, the account balance will be approximately $799.02 after 12 years.