Question

Oplease show the works.

Problem 4. A varying immediate annuity with a term of 2n years has a first payment equal to 1. Thereafter, payments increase by 1 each year until they reach n at the end of n years. Payments remain at n for year n + 1, and then decrease by 1 each year, with a final payment of 1 at the end of 2n years. Derive an expression for the present value of this annuity. (A) an (à – **) (B) a(2+) (C) a(a - ) (D) am (à + n) (E) a ml (1 + ante

Answer 1

Sol:- Given that :- A Vałying immediate annuity with a term of 20 years has a first payment equal to 1. Theater payments increase by each year until they reach n at the end of ń years. The annuity amounts to an n yood in annuity immediate starting at time o. plus an n year decreasing annuity immediate starting at time n. The present value of the sum of both is. :an? - VP+nV- van! = (1+i) az! - V"a7! = 25! (-y) 27: G ya) option (A) is correct answer,