Bob has offered Alice the choice between the following two options:

Option

A) Receive $10,000 in one year from today Option

B) Receive $500 every year starting one year from today

The interest rate is fixed at 5%. Alice wants to choose the option with the higher present value. Calculate the present value for each option and determine which option should she choose?

Solutions

Expert Solution

- Bob has two Options:-

Option A) Receive $10,000 in one year from today

Calculating the Present value of one time paymnet:-

Present Value = Future Value/(1+r)^n

Where,

r = Periodic Interest rate = 5%

n= no of periods = 1

Present Value = $10,000/(1+0.05)^1

Present Value = $9523.81

So, Present Value of Option A is $9523.81

Option B- Receive $500 every year starting one year from today

Calculating the Present value of perpetuity payment:-

Present value = Payment every year/Interest rate

Present value = $500/5%

Present value = $10,000

So, Present Value of Option B is $10,000

As the Present Value of Option B is greater than Option A, Option B should be chosen

jeff jeffy answered 2 years ago

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