Question

David won the lottery. He can take a single lump sum payout of $10 million dollars or receive $750,000 per year for the next 25 years. What rate of return would David need to break even if he took the lump sum amount instead of the annuity?a)6.19%b)5.31%c)4.98%d)5.56%

Answer 1

Option d

Explanation:

Given that David won the lottery. He can take a single lump sum payout of $10 million dollars or receive $750,000 per year for the next 25 years.

To break even both returns must be equal

Calculating 750000 every year for next 25 years would be equal to

`750000[1+(1+0.01r)+(1+0.01r)^2 +......(1+0.01r)^(25) }\\=750000[[(1+0.01r)^(25) -1](1)/(0.01r) \\`

This must equal 10 million dollars to break even

Equate and simplify to get

`([(1+0.01r)^(25))/(0.01r) =(10,000,000)/(750,000) =13.3333`

From annuity table we find that this approximately equals 5.56%

Hence option d

Answer 2

(d) 5.56%

Explanation:

In the question,

The amount David can take in lump sum = $10 million

or,

The amount he can receive for 25 years = $750,000/ year

Now,

If David need to take break after taking the lump sum amount is given by,

`(100000)/(750000)* 100=13.33\%`

Now,

From the Annuity table we can find out the value for the percent 13.33% for the time period of 25 years.

That is lying in between 5 and 6 tending towards 6 more.

So,

From the given options we can see that,

Rate of return can be = 5.56%

If the payment is made at the end of the year then only we can say that the rate of return is 5.56%.

Therefore, the correct option is (d).