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

Answer:

Option d

Step-by-step 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

$750000[1+(1+0.01r)+(1+0.01r)^2 +......(1+0.01r)^{25} }\\=750000[[(1+0.01r)^{25} -1]\frac{1}{0.01r}$

This must equal 10 million dollars to break even

Equate and simplify to get

$\frac{[(1+0.01r)^{25}}{0.01r} =\frac{10,000,000}{750,000} =13.3333$

From annuity table we find that this approximately equals 5.56%

Hence option d

Answer 2

Answer:

(d) 5.56%

Step-by-step 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,

$\frac{100000}{750000}\times 100=13.33\%$

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).