Answer to Question #257595 in Financial Math for zhidan

Question

A savings plan provides that in return for n annual premiums of X$, an investor will receive m annual payments of Y$ , the first such payments being made one period after payment of the last premium. Show that the equation of value can be written as either:

Ya(n+m)i −(X +Y)a(n)i = 0, or as (X +Y)s(m)i −Xs(n+m)i = 0

Suppose that X = 1.000, Y = 2.000, n = 10 and m = 10. Find the interest rate used in this transaction.

Answer 1

The value equation may be expressed as follows:

Ya(n+m)i - (X+Y)a(n)i =0

2a(10+10)i - (1.000+2.000)a(10)i= 0

2a(20)i - (3.000)a(10)i= 0

40ai - 30ai = 0

=10ai

(X + Y)s(m)i - Xs(n +m)i =0

(1.000+2.000)s(10)i - 1.000s (10 +10)i= 0

(3.000)s(10)i - 1.000s (20)i =0

30si - 20si =0

=10s

Therefore; 40ai - 30ai =10ai

30si - 20si=10ai