A perpetuity provides for continuous payments. The annual rate of payment at time t is { 1, 0 <= t <10 (1.03)^t-10, t >=10 Using an annual effective interest rate of 6%, the present value at time t = 0 of this perpetuity is x. Calculate X. a. 27.03 b. 30.29 c. 34.83 d. 38.64 e. 42.41

b. 30.29

Explanation:

Perpetuity is the state that lasts forever. In statistics the benefit that last for an indefinite period of time is calculated through perpetuity method.  

1/1.06 + 1/1.06^2 +1/1.06^3 + 1/1.06^4 + 1/1.06^5 + 1/1.06^6 + 1/1.06^7 + 1/1.06^8 + 1/1.06^9 =

0.942 + 0.893 + 0.87 + 0.821 + 0.791 + 0.752 + 0.691 + 0.652 + 0.604

=  7.017

7.017 / 0.23 = 30.29

answer; comparing the additional benefits and costs;