Answer:
At 6.31 % discount rate would you be indifferent between these two plans.
Explanation:
given data
plan x = $22,000
plan y = $32,000
time t = 19 year
solution
we will equate here both present value and that is express as
Present Value of Perpetuity = [tex]\frac{P}{r}[/tex] .................1
Present Value of Annuity = [tex]\frac{P}{r}(1 - (1 + r)^{-t})[/tex] .............2
equating both equation 1 and 2
[tex]\frac{P}{r}[/tex] = [tex]\frac{P}{r}(1 - (1 + r)^{-t})[/tex]
\frac{22000}{r} = \frac{32000}{r}(1 - (1 + r)^{-19})
(1 + r)^{-19} = 1 - \frac{22000}{32000}
solve it we get rate r
r = 0.063131
rate = 6.31 %
so at 6.31 % discount rate would you be indifferent between these two plans.
