Question

You win the lottery! Your choices are

• Take $25 million today.
• Take $1 million today and $1 million every year for the next 49 years (a total of $50 million)

a) If the interest rate is 0.1% compounded annually, which would you prefer?

b) If the interest rate is 4% compounded annually, which would you prefer?

c) At what annual interest rate would you be indifferent between the two?

use equation to solve!

Answer 1

Choice 1 : Take $25,000,000 today

Choice 2 : Take $1,000,000 today and $1,000,000 every year for next 49 years.

a) . If interest rate is 0.1% compounded annually :

Present value of Annual payments :-

At interest rate 0.01%, Choice 2 Annual Payments is better as it has higher present value.

b. If interest rate is 4% compounded annually

Present value of Annual payments :-

At interest rate 4%, Choice 1 lump-sum payment is better as it has higher value.

3. Annual interest rate that make indifferent between the two choices.

Let's first calculate the Present value at 3%

We have,

Lump-sum payment today = $25,000,000

PV of Annual payment at 3% = $26,501,656.93

PV of Annual Payment at 4% = $22,341,472.00

thus, Annual interest for indifferent between choices :

At 3.36% (approx) , Present value of Annual payments would be equals lump-sum payments.

Please note : This is an approx rate, We can get more accurate rate i.e 3.33% if we use excel or financial calculator.