Question

You have won a contest and are allowed to choose between two prizes. One option is to receive$200 today and another $200 one year from now. The second option is $100 today and anadditional $325 one year from now. At what interest rate (if any) is the present value of the twoprizes identical?A) 0 percentB) 5 percentC) 25 percentD)10 percentE) none of the above

Answer 1

Answer:C) 25 percent

Explanation:

option A

$200 now and another $200 one year from now

The Present value for this option = $200 + $200/(1 + r)

Option 2

$100 now and $325 one year from now

The Present Value for this option =  $100 + $325/(1 + r)

The question requires us to find an interest rate that will make the two prizes must be identical which means an interest that will make the present value of option A to be equal to the present value of option B

We therefore EQUATE present value formula for option A with present Value equation of option be and solve for variable " r "

$200 + $200/(1 + r) = $100 + $325/(1 + r)

100 + 325(1+r) = 200 + 200/(1 + r)

325/(1+r) = 200 + 200/(1+r) - 100 = 100 + 200/(1 + r)

325/(1 + r) = 100 + 200/(1 + r)

325/(1 + r ) = 100 x (1 + r)/(1 + r) + 200/(1+ r)

325/(1 + r) = (100 x (1 + r) + 200)/(1 + r)

cross multiply

(100 x (1 + r) + 200) x (1 + r) = 325 x (1 + r)

100(1+r)^2 + 200(1 + r) = 325(1 + r)

dividing the entire equation by (1 + r) we get

100(1 + r) + 200 = 325

100(1 + r) = 325 - 200 = 125

1 + r = 125/100 = 1.25

r = 1.25 - 1 = 0.25

R = 25%