what is the pv of an annuity due that promises to pay you $500 per yeaR FOR THE NExt 20 years if the interest rate is 7%?
If you put up $40,000 today in exchange for a 6.25 percent, 15-year annuity, what will the annual cash flow be?
To calculate the present value (PV) of an annuity due, we need to use the formula:
PV = PMT x ((1 - (1 + r)^(-n)) / r)
Where:
PV = Present Value
PMT = Payment per period
r = Interest rate per period
n = Total number of periods
In this case, the payment per year is $500, the interest rate is 7% (or 0.07 as a decimal), and the annuity lasts for 20 years.
First, let's convert the annual interest rate into a periodic interest rate. Since the payment is annual, we will use the same rate, which is 7%.
Now, substitute the values into the formula:
PV = $500 x ((1 - (1 + 0.07)^(-20)) / 0.07)
Calculate the values within the parentheses:
PV = $500 x ((1 - 1.07^(-20)) / 0.07)
Next, calculate the exponent:
PV = $500 x ((1 - 0.376889) / 0.07)
Subtract the value inside the parentheses:
PV = $500 x (0.623111 / 0.07)
Divide the numerator by the denominator:
PV = $500 x 8.901586
Finally, calculate the product:
PV = $4,450.79
Therefore, the present value (PV) of the annuity due promising to pay $500 per year for the next 20 years, with an interest rate of 7%, is approximately $4,450.79.