Given an interest rate of 7.2 percent per year, what is the value at Year 9 of a perpetual stream of $3,950 payments that begin at Year 19
To calculate the value at Year 9 of a perpetual stream of payments, we need to use the formula for the present value of a perpetuity.
The formula for the present value of a perpetuity is:
PV = P / r
where:
PV = Present Value
P = Payment per period
r = Interest rate per period
In this case, we have an annual interest rate of 7.2 percent, which means our interest rate per period is 7.2% / 100% = 0.072.
The payment per period is $3,950.
We want to find the present value at Year 9, so we need to calculate the present value of the payments at Year 9.
Let's calculate it step by step:
Step 1: Calculate the present value of the payments at Year 19
PV19 = P / r = $3,950 / 0.072
Step 2: Calculate the present value of the payments at Year 9
PV9 = PV19 / (1 + r)^(19-9)
The formula (1 + r)^(19-9) represents the factor by which we discount the payments from Year 19 to Year 9. We raise the factor to the power of (19 - 9) because we are discounting the payments for 10 years.
Step 3: Calculate the value at Year 9
The value at Year 9 is the present value of the payments at Year 9.
Value at Year 9 = PV9
Now, you can plug in the values and calculate the present value at Year 9.