Question

Randy has been awarded some money in a settlement. He has the option to take a lump sum payment of $300,000 or get paid an annuity of $2,000 per month for the next 20 years. Which is the better deal for Randy, and by how much, assuming the growth rate of the economy is 5.65% per year?

Answer 1

The answer choices are
Lump Sum: by $23,606.12
Lump Sum: by $16,726.56
Annuity: by $23,606.12
Annuity: by $16,726.56

Answer 2

So I would be using 300000=x*1.0565^20?

Answer 3

I got 99,938.1 but that does not make sens.

Answer 4

sense*

Answer 5

My thought is to compare present value of the lump sum (easy, it's 300,000) to the present value of the annuity

Answer 6

Ok. So what would I be doing?

Answer 7

2000((1+.0565)^(20)-1)/(.0565) I got 70,862.2

Answer 8

Finding the present value of the annuity is like the last problem, except the annuity is paid monthly, so the rate is 5.65%/12 or 0.0565/12
and n is 20*12= 240 payments

the first step is find the future value

Answer 9

yes, right idea, but you are doing payments once a year.

Answer 10

Ok. so it would be 2000((1+(.0565/12)^(20*12)-1)/(.0565/12)?

Answer 11

yes

Answer 12

So that would be 886708 so then it would be 886708-300000= 586708?

Answer 13

886708 is the future value. But to be fair we should compare its present value to 300,000

Answer 14

That is what I did right?

Answer 15

Or I could compare 886708-97167.3 which is 789540.7 which is making even less sense. What am I doing wrong?

Answer 16

where did you get 97167.3

Answer 17

300000=x*(1+(.0565/12))^240

Answer 18

300,000 is not the future value. It is a present value (how much you are paid right now)

Answer 19

300000*(1+(.0565/12))^240 is 926237.41

Answer 20

926237.41-886708= 39,529.41

Answer 21

But that is not close to any of the answers either.

Answer 22

yes I know. I was thinking, find the present value of the 886708, which I get to be
287197

but that leaves a difference between it and the lump sum of 300,000 - 287197= 12803
which does not match any of your choices.

Have you seen a problem like this before? If so, how do they solve it ?

Answer 23

I have not. This is the first time I am seeing this.. Let me look back in my textbook and see if I can see anything like it.

Answer 24

The three formulas that we are given is
Lump Sum
PV=FV/(1+i)^nt
ordinary Annuity
PVOA=c((1/i)-(1/(i(1+i)^nt)
annuity due
PVAD= c((1/i)-(1/(i(1+i)^nt)+c

Answer 25

I am assuming
assuming the growth rate of the economy is 5.65% per year?

means the interest rate is 5.65% But now I am wondering...

Answer 26

I think we are supposed to use PVOA. so it would be. 2000((1/(.0565/12))-(1/((.0565/12)(1+(.0565/12))^(12*20))= 287197 so 300000-287197= 12803 But that is not an answer either.

Answer 27

PVAD would be 289197 so 300000- 289197= 10803 which is not an answer wither so.

Answer 28

The 12803 is what I got, doing it the long way....

Answer 29

But that is not one of the options.

Answer 30

I have class in 2 hours so I can ask her about it specifically and let her know I cannot figure it out.

Answer 31

Does your book have any examples where they use "growth of the economy" Does it mean interest rate?

Answer 32

Let me see

Answer 33

There is this question

"Suppose Dimitri won a "lifetime of free groceries" contest in a random drawing at his local supermarket. The specific terms of his winnings are as follows: $2,000 in groceries, by each year's end, for the next 50 years. Dimitri is thrilled with this incredible prize! But he's curious: What would the value of this prize be if he simply received one cash payment now? Assume a 4.5% annual growth rate in the economy."

And they used PVOA to get 39542.02

Answer 34

yes, the PVOA matches my original thought. It might be you are a victim of a bad question?

I would show the teacher your work, and ask about the choices

Answer 35

Ok. I will ask her. I have class at noon. Thank you for all your trouble!

Answer 36

If you get an answer, please post it here, as I am curious.

Answer 37

To recap,

to compare a lump sum given immediately, to a payments stretched out over time,
convert the "annuity" to Present Value (how much it is worth right now)
then compare Present Value to the lump sum.

Answer 38

Ok. I will post the answer when I find out! And I will ask her for help.

Answer 39

When I use the site
http://www.bankrate.com/calculators/investing/annuity-calculator.aspx
with
Withdrawal Amount: $2000.00 Annual Growth Rate: 5.65%
Interval Between Withdrawals: Monthly Length of Annuity: 20 years
Starting Principal: $288548.94

It finds 288548.94. This is 300,000-288548.94= 11451.06 less than the lump sum. This does not match any of your choices.

Answer 40

My teacher thinks there is a flaw in the question. She could not get the answer they were asking for.