time value of money

panda125

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Oct 1, 2010
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You have just won the lotto, you have two options, you can receive ten, 500,000 dollars semiannual payments starting today, or you can take your winning in a lump-sum payment now based on 7% annual interest rate. Determine the equivalent lump-sum payment?

Hi, im really having a hard time trying to solve this problem. I believe the first options is a annuity due, since the payments are starting today, but what really confuses me is the ten semiannual payments. Also the second option do i just take the 500,000 dollars with the ten payments and 7% interest and just figure out the present value of a dollar?
 
panda125 said:
You have just won the lotto, you have two options, you can receive ten, 500,000 dollars semiannual payments starting today, or you can take your winning in a lump-sum payment now based on 7% annual interest rate. Determine the equivalent lump-sum payment?
HINT: equivalent lump-sum payment = 500000 + PV(9 semiannual payments of 500000, i = .035)
 
500,000+366,865= 733,730

Pv = 366,865
Is the answer 733,730 ?
And also why would I have 9 semi annual payments ?
 
panda125 said:
500,000+366,865= 733,730

Pv = 366,865
Is the answer 733,730 ?
And also why would I have 9 semi annual payments ?

..... you can receive ten, 500,000 dollars semiannual payments starting today......
 
see I can change the color of my text too, but it doesn't help the situation out.
 
panda125 said:
see I can change the color of my text too, but it doesn't help the situation out.

If you were given one payment (out of ten) today - how many payments are left ?

For some, changing color does not help - "thinking and working" on the other hand helps everybody...
 
panda125 said:
500,000+366,865= 733,730
Pv = 366,865
Is the answer 733,730 ?
And also why would I have 9 semi annual payments ?
RELAX Panda!
You've won $5 million bucks and are willing to accept only $733,730? :shock:

I showed you this:
HINT: equivalent lump-sum payment = 500000 + PV(9 semiannual payments of 500000, i = .035)
That's not 9, but 10 payments: 500,000 NOW, then 9 every 6 months; OK?

Do you know how to get the Present Value of a series of future payments?
Apparently not: are these formulas not given to you by your teacher?

Here's the formula:
PV = p[1 - 1/(1 + i)^n] / i
where:
p = payment amount (500000)
i = interest rate (.035)
n = number of payments (9)

Ya'll ok now?
 
Thank you for your help, i really appreciate it, in our class we use tables that correspond to the N and I, so it really makes it hard to double check answers.

With your explanation, i perform the pv= 500000[1 - 1/(1 + .035)^9] / .035, which gives me 3,803,840
 
panda125 said:
Thank you for your help, i really appreciate it, in our class we use tables that correspond to the N and I, so it really makes it hard to double check answers.

With your explanation, i perform the pv= 500000[1 - 1/(1 + .035)^9] / .035, which gives me 3,803,840
3,803,843.25 to be exact...
Don't forget that the TOTAL you'd get is 3,803,843.25 + 500,000.00 ; ok?
 
yes i understand, the only thing im a little confuse about is the how the payments are received.

Since the payment starts today, why wouldn't this be a annuity due, in which i would take the 3,803,843 and multiple it by (1+i), then add it to 500,000
 
actually since the question is asking for a equivalent lump-sum payment, couldn't i take the Fv of 5,000,000 and use the 7 percent interest given and turn the 10 semi annual payments to 5 annual payments and use the present value formula fv/(1+i)^n to determine the one lump sum payment

n=5
i=7
fv= 5,000,000
 
panda125 said:
actually since the question is asking for a equivalent lump-sum payment, couldn't i take the Fv of 5,000,000 and use the 7 percent interest given and turn the 10 semi annual payments to 5 annual payments and use the present value formula fv/(1+i)^n to determine the one lump sum payment
NO! $5 million is NOT a future value...

Here's how this works:
Code:
      PAYMENT     INTEREST      BALANCE
0                            4,303,843.25*
0  -500,000.00         .00   3,803,843.25*
1  -500,000.00  133,134.51** 3,436,977.76
2  -500,000.00  120,294.22   3,057,271.98
....
8  -500,000.00   33,244.65     483,091.78
9  -500,000.00   16,908.22            .00
* PV is either of these, depending on how you look at it:
an annuity immediate, or getting the annuity after receiving $500,000 : same thing...

** 3803843.25 (.035) = 133134.51 : calculating interest for 6 months
 
so in theory i could have take n=10 i=.035 and taken the 500,000 and figure out the annuity due formula , which would give me the same answer
 
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