Calculate the single risk premium (to 2 decimal places) to be charged today on an insurance product that pays regular claims of $500 in 1,2,3,...,25 years from today. Use an interest rate of 4% per annum.
200
To calculate the single risk premium for the insurance product, we need to determine the present value of each future claim and then sum them up.
The present value of a future claim is calculated using the formula:
PV = CF / (1 + r)^n
Where:
PV = Present Value
CF = Cash Flow (in this case, the future claim amount of $500)
r = Interest Rate (expressed as a decimal)
n = Number of years in the future
Given that the interest rate, r, is 4% per annum (or 0.04 as a decimal), we can calculate the present value of each claim and then sum them up to find the single risk premium.
Let's calculate the present value for each claim:
PV(1 year) = 500 / (1 + 0.04)^1
PV(2 years) = 500 / (1 + 0.04)^2
PV(3 years) = 500 / (1 + 0.04)^3
...
PV(25 years) = 500 / (1 + 0.04)^25
Now, let's calculate the present value for each claim using the formula:
PV(1 year) = 500 / (1 + 0.04)^1 = 500 / 1.04 ≈ 480.77
PV(2 years) = 500 / (1 + 0.04)^2 = 500 / 1.0816 ≈ 462.91
PV(3 years) = 500 / (1 + 0.04)^3 = 500 / 1.1249 ≈ 445.16
...
PV(25 years) = 500 / (1 + 0.04)^25 = 500 / 2.3669 ≈ 211.28
Finally, sum up all the present values to get the single risk premium:
Risk Premium = PV(1 year) + PV(2 years) + PV(3 years) + ... + PV(25 years)
Risk Premium ≈ 480.77 + 462.91 + 445.16 + ... + 211.28
Calculating this sum will give you the final single risk premium for the insurance product.