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.

[Actuwhat?]

---> 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

[Actuwhat?]

It messed up my time diagram...sorry

Ah. I get the idea. Thanks actuwhat? !

[RG]

Just in case -

You DO know that your calculator will do this for you? Mine spits out 7.948564428. This is a BA II-plus.

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

Originally Posted by RG

Just in case -

You DO know that your calculator will do this for you? Mine spits out 7.948564428. This is a BA II-plus.

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

I couldn't see a way to use the cash flow or time value of money functionality of the BA-II Plus to solve it. How do you do it? The interest rate should work out to 9.09%, I believe.

[Wannabe Actuary]

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 BA-35 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!

[RG]

Woops, I had read 141, not 144.

On the BA II-Plus, 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

Thanks RG.