Question

Which do you prefer of the options below? Is there an interest rate at which you switch your preference? If so, what is the rate at which the switch occurs?
Option 6: $100 every 2 years with the first payment in 1.5 years plus $50 every two years with the first payment in 3 years.
Option 7: $50 every two years with the first payment in 1 year plus $100 every two years with the first payment in 2.5 years.

Answer 1

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

$\frac{100}{r} (1+r)^{-1.5}$

perpetuity of 50 every 3 years discounted 3 years

as the payment are every three years we calcualte an equivalent rate:

$(1+r)^{3} -1 =r_e$

$\frac{50}{(1+r)^{3} -1} (1+r)^{-1.5}$

Option 7

perpetuity of 50 discounted 1 year

$\frac{50}{r} (1+r)^{-1}$

perpetuity of 100 every 2 years discounted 2.5 years

equivalent biannual rate

$(1+r)^{2} -1 =r_e$

$\frac{100}{(1+r)^{2} -1} (1+r)^{-2.5}$

having the formulas

we can do it on excel solver to look at which rate the switch produces