Calculate the present value of the annuity. (Round your answer to the nearest cent.)
$1600 monthly at 6.6% for 30 years.
Using the formula that you must know:
PV = payment( 1 - (1+i)^-n )/i
i = .066, n = 30
plug in those values in your calculator and calculate.
Let me know what you got.
To calculate the present value of an annuity, you can use the formula:
PV = P * (1 - (1 + r)^(-n)) / r
Where:
PV is the present value of the annuity,
P is the periodic payment,
r is the interest rate per period,
n is the number of periods.
In this case, the periodic payment (P) is $1600, the interest rate per period (r) is 6.6% or 0.066, and the number of periods (n) is 30 years.
First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate would be 6.6% / 12 = 0.55%/month or 0.0055.
Now, we can substitute the values into the formula:
PV = $1600 * (1 - (1 + 0.0055)^(-30)) / 0.0055
Using a calculator, we can simplify the expression inside the parentheses:
PV = $1600 * (1 - (1.0055)^(-30)) / 0.0055
Then, you can substitute the values and calculate:
PV = $1600 * (1 - 0.597454) / 0.0055
PV = $1600 * 0.402546 / 0.0055
PV ≈ $116,230.18
Therefore, the present value of the annuity is approximately $116,230.18.