What is the present value of a security that will pay $5,000 in 20 years if securities of equal risk pay 7% annually?
What is
5000(1.07)^-20 ?
To calculate the present value of the security, we can use the formula for the present value of a future cash flow:
Present Value = Future Value / (1 + Interest Rate)^Time
In this case, the Future Value is $5,000, the Interest Rate is 7% per year, and the Time is 20 years. Plugging in these values, we get:
Present Value = $5,000 / (1 + 0.07)^20
Now, let's solve this equation step-by-step:
Step 1: Calculate the interest rate in decimal form.
Interest Rate = 7% / 100 = 0.07
Step 2: Calculate the denominator of the equation.
Denominator = (1 + 0.07)^20
Step 3: Calculate the denominator value.
Denominator = (1.07)^20 ≈ 3.8697
Step 4: Divide the Future Value by the denominator to find the Present Value.
Present Value = $5,000 / 3.8697 ≈ $1,291.18
Therefore, the present value of the security that will pay $5,000 in 20 years, assuming a 7% annual interest rate, is approximately $1,291.18.
To calculate the present value of a future payment, we need to use the concept of time value of money. The formula used to calculate the present value is:
PV = FV / (1 + r)^n
Where:
PV = Present value
FV = Future value
r = Interest rate per period
n = Number of periods
In this case, the future value (FV) is $5,000, the interest rate (r) is 7% annually, and the number of periods (n) is 20 years.
We can plug these values into the formula to calculate the present value:
PV = $5,000 / (1 + 0.07)^20
To evaluate this calculation, we can simplify it step by step. First, we calculate the value within the parentheses:
(1 + 0.07)^20 = 2.653297...
Then, we divide $5,000 by this value:
PV = $5,000 / 2.653297...
Calculating this division, we find:
PV ≈ $1,885.84
Therefore, the present value of a security that will pay $5,000 in 20 years, assuming securities of equal risk pay 7% annually, is approximately $1,885.84.