What is the present value of nine annual cash payments of $4,000, to be paid
at the end of each year using an interest rate of 6%?
27,607.00
To calculate the present value of future cash payments, you can use the present value formula. The formula for present value is:
PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + ... + CFn / (1 + r)^n
Where:
PV = Present Value
CF = Cash Flow
r = Interest Rate
n = Number of periods
In this case, the cash flow is $4,000, the interest rate is 6%, and the cash payments occur annually for nine years. Let's substitute these values into the formula:
PV = $4,000 / (1 + 0.06)^1 + $4,000 / (1 + 0.06)^2 + ... + $4,000 / (1 + 0.06)^9
Now, let's calculate the present value by evaluating each term in the formula:
PV = $4,000 / (1.06)^1 + $4,000 / (1.06)^2 + ... + $4,000 / (1.06)^9
Simplifying each term:
PV = $4,000 / 1.06 + $4,000 / (1.06)^2 + ... + $4,000 / (1.06)^9
Now compute each term:
PV = $3,773.58 + $3,559.21 + $3,352.30 + $3,152.15 + $2,958.16 + $2,769.88 + $2,586.90 + $2,408.80 + $2,235.20
Adding them up:
PV = $28,836.28
Therefore, the present value of nine annual cash payments of $4,000, to be paid at the end of each year using an interest rate of 6%, is $28,836.28.