Answer:
As the first payment occurs on option 7 n interest rate higher enough can make the 50 dollars received first make the difference.
The switch produced at a rate of :
300%
Interest rate below this mark favor option 6
while higher than this favor option 7
Explanation:
Option 6
perpetuity of 100 discounted 1.5 year
[tex]\frac{100}{r} (1+r)^{-1.5}[/tex]
perpetuity of 50 every 3 years discounted 3 years
as the payment are every three years we calcualte an equivalent rate:
[tex](1+r)^{3} -1 =r_e[/tex]
[tex]\frac{50}{(1+r)^{3} -1} (1+r)^{-1.5}[/tex]
Option 7
perpetuity of 50 discounted 1 year
[tex]\frac{50}{r} (1+r)^{-1}[/tex]
perpetuity of 100 every 2 years discounted 2.5 years
equivalent biannual rate
[tex](1+r)^{2} -1 =r_e[/tex]
[tex]\frac{100}{(1+r)^{2} -1} (1+r)^{-2.5}[/tex]
having the formulas
we can do it on excel solver to look at which rate the switch produces
