Question

Present Value/Future Value Question

I haven't gotten an answer on openstudy in a week.
If you do answer this correctly ,I'll give you a fan, a medal and a testimony.

Answer 1

Ralph has been awarded some money in a settlement. He has the option to take a lump sum payment of $425,000 or get paid an annuity of $2,000 per month for the next 25 years. Which is the better deal for Ralph, and by how much, assuming the growth rate of the economy is 5.15% per year?

Lump Sum: by $91,772.64

Lump Sum: by $34,251.30

Annuity: by $91,772.64

Annuity: by $34,251.30

Answer 2

Lump sum formula

FV
PV = ________
(1 + i)^nt

Answer 3

Annuity Formula

http://prntscr.com/apd6lc

Answer 4

I think I can help

Answer 5

You know how to plug in the $425,000 into the formula, right?

Answer 6

no.

Answer 7

PV= past value while FV = future value

Answer 8

PV = Present value
which is what I'm looking for lol

Answer 9

Oops, yeah I meant that lol

Answer 10

Well currently, our present value is f $425,000

Answer 11

We dont have the FV so you''ll have to reverse the equation to get that.

Answer 12

you don't need those formula, you can make it up.

each payment of USD2,000 just needs to be discounted.

the discount rate is monthly, use \(i = {5.15 \% \over 12}\) even though strictly speaking you should solve \((1+i)^{1/12} = 105.15\) to get a true compounded rate.

[the diff between the 2 is c.\(0.01 \%\).]


assume the first instalment is paid immediately, so not discounted. every other payment needs to be discounted at the prevailing reinvestment rate over the period for which it is extant....

the cashflow when discounted looks like this

\(2000 \left( 1 + \dfrac{1}{1 + i} + \dfrac{1}{(1 + i)^2} + \dfrac{1}{(1 + i)^3} + \dots + \dfrac{1}{(1 + i)^{(25\times 12) - 1}} \right)\)

so the common ratio for the geometric series is \(r = \dfrac{1}{1 + i}\)

\(S = a \dfrac{1-r^n}{1-r}\)

\(n = 25 \times 12\)

I get USD 338, 509 for the annuity, so take the cash!!!

hope that's right

Answer 13

The closest answer to that is D
Annuity: by $34,251.30

Answer 14

Is that good @IrishBoy123 ?

Answer 15

the cash is better by ~$86k or ~$88k depending on whether i do it my way or just plug into their formula. ie even the formaulae they invite you to use don't give an exact match.

so A is the **closest** answer.....IMHO