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#1




Present value problem, easier solution?
Here's a problem that I'm looking for an easier way to solve:
At an effective annual interest rate of i, i >0, each of the following two sets of paymtents has a present value of K: i) a payment of 121 immediately and another payment of 121 at the end of one year. ii) A payment of 144 at the end of two years and another payment of 144 at the end of three years. Calculate K. (answer 232)  So, I set up 121 + 121 / (1+i) = 144 / (1 + i)^2 + 144 / (1 + i)^3 Is there an easy way to solve for i? I applied Newton's method and got the answer, but I'm looking for an easier way. 
#2




solution
> 121 > 121>
(it accumulates to t=1) then move the lump forward 2 years  0 1 2 3 > 141 > 141 (right side of equation) I will denote s angle n as s(n) 121s(2)*(1+i)^2 = 141s(2) now cancel the s(2) on each side AND divide the 121: (1+i)^2 = 141/121 i = sqrt(141/121)1
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#3




It messed up my time diagram...sorry
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#4




Ah. I get the idea. Thanks actuwhat? !

#5




Just in case 
You DO know that your calculator will do this for you? Mine spits out 7.948564428. This is a BA IIplus. Also  obviously with a MC exam, you just try a few of the answer choices, though that's easiest once you've simplified like actuwhat 
#6




Quote:

#7




Of course if can be done similar to what Actuwhat did as well.
You can use the annuity due function (a dot n  hopefully that's understandable, damn math formulas are impossible to type) and look at everything in that mind set and evaluate at t=0. So you have 121 (a dot 2) = [144 (a dot 2)] / (1 + i)^2 This leads you to the same (1 + i)^2 = 144/121 that Actuwhat shows, but I think this way was more intuitive, given the first stream of payments. It's all a matter of what you're more comfortable with. And this gives you i = 9.09 or so, but once you solve for that answer just store it as i in your calculator and use the annuity due function (very easy on BA35 solar), with 2 payments of 121 along with the i you just stored and have it compute PV. Spits back just under 232. Calculators are great, aren't they! 
#8




Woops, I had read 141, not 144.
On the BA IIPlus, it's the 2nd line of buttons: CF stands for cash flow, NPV and IRR are what you think they are. Look at the manual if this is confusing, but here's this problem: cf displays cf0=, which we set to 121, enter, down arrow, displays cf1=, which we set to 121, enter, down arrow, which displays f01=1, which is fine, down arrow, displays cf2=0; set it to 144 and f02 to 2. Then hit IRR and compute to get 9.090909091 Then to find NPV of either set of payments, delete the other: I set cf2=0; hit npv and set i=9.0909091, down arrow, npv= compute to get 231.9166667 
#9




Thanks RG.

#10




Quote:
Why set 144 to be negative? 
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