Max has just won some money on a game show! He has the option to take a lump sum payment of $500,000 now or get paid an annuity of $4,900 per month for the next 10 years. Assuming the growth rate of the economy is 2.9% compounding annually over the next 10 years, which is the better deal for Max and by how much?

Question

ganeshie8 · Answer

use the Present Value formula for annuity

anonymous · Answer

attachment

ganeshie8 · Answer

Present Value =  $\large C\left(\dfrac{1}{i} - \dfrac{1}{i(1+i)^{nt}}\right)  $

ganeshie8 · Answer

^^this one..

ganeshie8 · Answer

its an annuity cuz he is getting money each month...

anonymous · Answer

PV= 500,000(1/.29-1/.29(1+.29)^120)

anonymous · Answer

Is that right?

ganeshie8 · Answer

Nope

anonymous · Answer

Is it all wrong? D:

ganeshie8 · Answer

you should get :

Present Value =  $\large 4900*12*\left(\dfrac{1}{0.029} - \dfrac{1}{0.029(1+0.029)^{10}}\right)  $

ganeshie8 · Answer

yearly u are getting a payment of 4900*12,
so, $\large   C =   4900*12$

ganeshie8 · Answer

since this in annual compounding, $n = 1$
 So,   $\large  i = \frac{r}{n} =   0.029$

ganeshie8 · Answer

evaluate and see how much u get for Present Value of this annuity

ganeshie8 · Answer

compare it with the lump sum payment of  $500,000 and decide

anonymous · Answer

670980?

ganeshie8 · Answer

nope

ganeshie8 · Answer

http://www.wolframalpha.com/input/?i=4900*12*%5Cleft%28%5Cdfrac%7B1%7D%7B0.029%7D+-+%5Cdfrac%7B1%7D%7B0.029%281%2B0.029%29%5E%7B10%7D%7D%5Cright%29++

ganeshie8 · Answer

wolfram says, $504,145

ganeshie8 · Answer

^^

anonymous · Answer

ohh okay so a. Lump Sum: by $77,462.75
b. Lump Sum: by $4,145.41
c. Annuity: by $88,000.00
d. Annuity: by $4,145.41
it would be b then?

anonymous · Answer

no sorry it would be D

ganeshie8 · Answer

Yes ! Annuity pays more here so it would be D