Prizewinner in a sweepstakes.

maxitronixy · Jun 21, 2009

ah my bad

PragmaticIdeals · Jun 21, 2009

This question is flawed... there's no right answer (it's ALMOST 21.6 though)...

To solve you just use the equation:

50 x (1 + i)^2 + 50 x (1 + i) + 50 = 125 x (1 + i)^2

and solve for i

turns out to be 21.525% ...

GFX007 · Jun 21, 2009

Quote from trendy:

The answer is C, 21.6%

OK, you have two $50,000 payments over two years. The question is what interest rate is needed on those two payments over the two years to equal the PV (present value) of $75,000. Why $75,000? Because that's the difference between the $125,000 now payment, and the first $50,000 payment which is also paid immediately. The answer is 21.525% Rounded to 21.6%

To verify, take $125,000 and calculate the FV (future value) in two years using 21.6% interest. ($184,832)

Then, calculate FV of $50,000 for two years using 21.6, then add FV of $50,000 @21.6 interest for one year, then add $50,000. ($184,832)

But how did you solve it to get the value 21.525 (21.6) ?

PragmaticIdeals · Jun 21, 2009

Quote from GFX007:

But how did you solve it to get the value 21.525 (21.6) ?

See the equation I set up.

GFX007 · Jun 21, 2009

Quote from PragmaticIdeals:

See the equation I set up.

Can it be done this way?
I've seen some similar questions solved this way:

Cash flow Diagram:

125m
^
|
50m````A=50m
|.........|.........|
|.........|.........|
-----------------
0.......1.........n=2

P = A (P/A, i%, n)
175m = 50m (P/A, i%, 2)
3.5 = (P/A, i%, 2)

And then use the Discrete Compounding Interest Table to find where it fits? And then use Linear Interpolation to find i ?

PragmaticIdeals · Jun 21, 2009

Quote from GFX007:

Can it be done this way?
I've seen some similar questions solved this way:

Cash flow Diagram:

125m
^
|
50m````A=50m
|.........|.........|
|.........|.........|
-----------------
0.......1.........n=2

P = A (P/A, i%, n)
145m = 50m (P/A, i%, 2)
2.9 = (P/A, i%, 2)

And then use the Discrete Compounding Interest Table to find where it fits? And then use Linear Interpolation to find i ?

Hmm..

Does not compute.

GFX007 · Jun 21, 2009

Quote from PragmaticIdeals:

Hmm..

Does not compute.

my bad...

i edited this part

m (shorthand for 1000)

P = 125,000 + 50,000 = 175,000

P = A (P/A, i%, n)
175,000 = 50,000 (P/A, i%, 2)
3.5 = (P/A, i%, 2)

TGregg · Jun 22, 2009

Quote from PragmaticIdeals:

This question is flawed... there's no right answer (it's ALMOST 21.6 though)...

That's the thing. There are two problems. First is, they ask for a rate, not a yield. Perhaps it's simple interest. The OP can shed some light, if he has no idea what e is or how to figure continuous yield from a rate then it is probably simple interest.

The other problem is, 25.5% is closer to the exact answer than 25.6. Perhaps there was an understanding of rounding up, but otherwise the answer of 25.6 is out of tolerance.

Interestingly, 19.5% as a rate works. I still wonder if the first choice was supposed to be 19.5 instead of 15.5.

PragmaticIdeals · Jun 22, 2009

Quote from TGregg:

That's the thing. There are two problems. First is, they ask for a rate, not a yield. Perhaps it's simple interest. The OP can shed some light, if he has no idea what e is or how to figure continuous yield from a rate then it is probably simple interest.

The other problem is, 25.5% is closer to the exact answer than 25.6. Perhaps there was an understanding of rounding up, but otherwise the answer of 25.6 is out of tolerance.

Interestingly, 19.5% as a rate works. I still wonder if the first choice was supposed to be 19.5 instead of 15.5.

How does 19.5 work?

And you mean 21.5 and not 25.5 right?

TGregg · Jun 22, 2009

Quote from PragmaticIdeals:

How does 19.5 work?

And you mean 21.5 and not 25.5 right?

Yeah, 21.5

(e^(21.52. . .)) -1 = ~19.5%
Whoops, that's backwrds. Too much crap going on. Reverse it:

(e^(~19.5)) -1 = 21.52. . .

Using a compounded continuously rate of 19.5%, you end up with $224,373.8732 taking $125k on day 1 and $224,364.1383 taking 3 payments of 50k. Less than $10 difference. Using a yield of 21.6% produces 224755.712 and 224635.0848 for a difference of ~$120. A yield of 21.5% produces a difference of ~$40.