An oil company has to pay $10000 per year starting one years from today on a loan obtain for 5 years at an effective interest rate of 8%.
Calculate the equivalent present value of this 5 yearly annuity.?
To calculate the equivalent present value of a 5-year annuity, we need to discount each payment back to its present value using the effective interest rate of 8%.
Step 1: Find the discount factor:
The discount factor is calculated using the formula:
Discount factor = 1 / (1 + r)^n
where:
r is the effective interest rate and
n is the number of years.
In this case, the effective interest rate is 8% (or 0.08 in decimal form), and the number of years is 5.
Discount factor = 1 / (1 + 0.08)^5
Discount factor = 1 / (1.08)^5
Discount factor = 1 / 1.4693
Discount factor = 0.6806
Step 2: Calculate the present value of the annuity:
To find the equivalent present value of the 5-year annuity, multiply the annual payment amount by the discount factor.
Present value = Annual payment * Discount factor
Present value = $10,000 * 0.6806
Present value ≈ $6,806
Therefore, the equivalent present value of this 5-year annuity is approximately $6,806.