what is the present value of a perpetuity of $2500 per year given an interest rate of 8.25% p.a? (assume the first cash is four years from today)
The assumption that the first payment is made 4 years from now should have been an essential part of the question, not an afterthought in brackets.
So three years from now there has to be sufficient money in the fund to provide interest of 2500 in one year.
P=I/(rt) = 2500/.0825 = $30,303.03
how much is that worth now ?
Present Value = 30303.03(1.0825)^-3
= $23,889.24
To calculate the present value of a perpetuity, you need to use the formula:
Present Value = Cash flow / Interest rate
In this case, the cash flow is $2,500 per year, and the interest rate is 8.25% per annum. However, since the first cash flow occurs four years from today, we need to account for this delay in the calculation.
Here are the steps to calculate the present value of a perpetuity:
Step 1: Convert the interest rate to a decimal:
Interest rate = 8.25% = 0.0825
Step 2: Calculate the present value:
Present Value = $2,500 / (1 + Interest rate)^n
Where 'n' represents the time in years until the first cash flow occurs. In this case, n = 4.
Substituting the values into the formula:
Present Value = $2,500 / (1 + 0.0825)^4
Calculating the numerator:
$2,500 / (1.0825)^4
Calculating the denominator:
$2,500 / 1.3666
Calculating the present value:
Present Value ≈ $1,830.79
Therefore, the present value of a perpetuity of $2,500 per year, with an interest rate of 8.25% per annum, and the first cash flow occurring four years from today is approximately $1,830.79.