Find the present value of lottery winnings

[isukatphysics69]

Homework Statement

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Homework Equations

in picture

The Attempt at a Solution

(200000(1-0.96^19))/(1-0.96) = 2697903.99

not sure what i did wrong here, answer seems close.

 

[StoneTemplePython]

check your underlying math...
1.)
$\frac{1}{1.04} \gt 0.96$

2.)
also note the different indexing in the finite series up top vs the problem you are asked to solve.

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You are suppose to show some more work than this, I think, though I know in a lot of finance courses they don't make you derive / telescope the finite geometric series.

 

[Ray Vickson]

Homework Statement

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View attachment 225578

Homework Equations

in picture

The Attempt at a Solution

(200000(1-0.96^19))/(1-0.96) = 2697903.99

not sure what i did wrong here, answer seems close.

(1) 1/1.04 ≠ 0.96. The differences are large enough to throw off the answer by almost $40,000, using exactly the same formula for the sum.
(2) Your sum formula is wrong: you are using the formula for $\sum_{n=0}^{19}$ when you should be doing $\sum_{n=1}^{20}$. That throws you off by about another $109,000.

So: keep more decimal places in intermediate computations. Using 1/1.04 ≈ .9615384615 will do the job. Nowadays, with good hand-held calculators and computers there is no reason to round off so much, at least until the job is done.

BTW: do not be mis-lead by typical advice to keep only as many significant figures as the data: you should round off at the END of a calculation, not during it. Besides, the 1.04 is not really just a 3 sig-fig number; it is actually accurate to infinitely many decimal places, since the 4% is accurate (the "4" is an integer, not a floating-point number) and so your 1.04 is really 1 + (4/100) = 104/100 EXACTLY.

Financial calculations are not like calculations in physics; if a financial institution says that an interest rate is 3.95%, it means that the interest rate is 0.03950000... = 395/1000 with absolute accuracy, and it will typically carry out calculations of multi-million dollar amounts down to the nearest penny. Financial computations don't usually involve the concept of "significant figures" at all!