Question

Oxana recently won $100,000 in the lottery. She has the option of receiving the entire $100,000 today or she can receive two payments of $51,500 one year apart, with the first one today (so $51,500 today and another $51,500 in one year). For simplicity, assume that lottery winnings are not taxed and that there is no inflation.

Suppose the interest rate is 4%. Which option should Oxana choose?

Suppose the interest rate is 0%. Which option should Oxana choose?

What interest rate will make Oxana indifferent between the two payment schemes? Give your answer to two decimal places.

Answer 1

If the interest rate is 4%,

The present value of the money received would be in 2 different payments = 51500 + 51500 / 1.04

= $101019.23

As the present value is more than $100,000 , it would be better choose the option of 2 payments.

If the interest rate is 0%, the present value of the two payments = 51500 + 51500/1.00

= $103000

As the present value is more than $100,000 , it would be better choose the option of 2 payments.

To find the interest rate, at which both the options are equally viable =

Let the interest rate be i.

So, the equation would be ,

100000 = 51500 + 51500/(1+i)

=> 48500 = 51500/ (1+i)

=> i = 0.06185

= i = 6.185%

So, the rate of interest at which both the options would be equal will be 6.185%.

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