Question

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.

Answer 1

The single risk premium is calculated by finding the present value of each $500 claim to be paid over the next 25 years at a 4% annual interest rate and summing these values.

Step-by-step explanation:

To calculate the single risk premium to be charged today on an insurance product that pays regular claims of $500 for each of the next 25 years at an interest rate of 4% per annum, we need to calculate the present value of each of those payments and then sum them up. This can be done using the present value formula for each individual payment:

Present Value (PV) = Payment / (1 + r)^t

Where 'r' is the interest rate (4% or 0.04 in decimal form) and 't' is the number of years until the payment is made.

To calculate the sum:

1. 
   
3. Calculate the present value of each $500 payment this way:
4. 
   
6. PV1 = 500 / (1 + 0.04)^1
7. 
   
9. PV2 = 500 / (1 + 0.04)^2
10. 
    
12. ...
13. 
    
15. PV25 = 500 / (1 + 0.04)^25
16. 
    
18. Sum all present values to get the total present value:
19. 
    
21. Total PV = PV1 + PV2 + ... + PV25

The total of these present values will be the amount of the risk premium that should be charged today to cover the claims.

Answer 2

We are given with the following:
A = 500
n = 25
i = 0.04

We solve for the single risk premium by this formula:
P = A [(1 + i)^n - 1] / [ i (1 + i)^n]
P = 500 [(1 + 0.04)^25 - 1] / [0.04 (1 + 0.04)^25]
P = 78111.04

The premium is $78,111.04.