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View Full Version : Course 2: Averbach and Mehta problem 18

KnightsPG
08-21-2002, 11:16 AM
A bank charges interest of 5% per year, compounded semiannually, for the next two years. After that, the interest rate is 8% per year, compounded semiannually. Theda borrows 5,000 to be repaid in 14 payments, with level payments at the end of each half year for the next 7 years. What is the amount of each semiannual payment?

I can get the problem set up. I understand that for the first 2 years the interest rate for each half year is 2.4695077% or 2.5% and the next 5 years the interest rate for each half year is 3.9230485% or 4%.

So for the first 4 time intervals (each half year), N=4, i = 2.5%, and for the next 10 intervals, n=10, i=4%.

5000=x[a(4|2.5%) + (1.025)^-4* a(10|4%)] = x(11.11)

x = 450.045

The problem I have had is figuring out how to get x(11.11) from the ugly annuity summation. Is there any easy way to do this? Obviously, I could slowly with my calculator figure out v+v^2+... one by one, but I'm guessing there may be an easier formula that I may have missed. Can anyone help me out? Thanks in advance for your help!

c3 taker
08-21-2002, 12:18 PM
Knights PG......if you have the BA-35 calculator it's easy. Your first term is a<sub>4</sub> so for that you type into your calculator:
4 [N]
2.5 [i]
1 [pmt]

[calc] (I think it's a second function then the button next to it, i dont' have my calculator handy) [PV]

That will give you the annuity factor. Do that for each piece, multiply the second one by v<sup>4</sup> and add them together to get 11.11.

You can still do it with no calculator but you have to plug i into the anniuty formula which is (1 - v<sup>n</sup>) / i

You hardest part of that problem is setting up the equation. Once you do that it's no sweat.

Hope I could help :)

MathGuy
08-21-2002, 12:19 PM
BA calculators are for babies too...

KnightsPG
08-21-2002, 12:36 PM
C2 Taker-

Thanks for the help. I figured there was an easy shortcut using the calculator. These problems will be easy now on. Thanks.

c3 taker
08-21-2002, 12:49 PM
BA calculators are for babies too...

fine by me if you want to scribble down all the formulas and do it by hand....no wait you don't belive in formulas either.....but I'll stick with the calculator whether they are for babies or not

bg23516
08-21-2002, 01:39 PM
Make a conscious effort to understand the formulas, where they came from, etc. Understand your principles. Then, learn to use the calculator. Learn it WELL. It can be used for many many problems, and can dramatically shorten time to do a problem.

It doesn't matter if you can derive every formula you need if you can't finish the exam.

VernSchil
08-21-2002, 02:20 PM
Just how important is it to memorize interest formulas that in practice are rendered useless by calculators like the BA-35? ie. Are there ever any problems on Course 2 that would REQUIRE specific application of formulas such as the PV of an annuity and would NOT be solvable with the easy annuity functions of the calculator?

c3 taker
08-21-2002, 02:39 PM
Just how important is it to memorize interest formulas that in practice are rendered useless by calculators like the BA-35? ie. Are there ever any problems on Course 2 that would REQUIRE specific application of formulas such as the PV of an annuity and would NOT be solvable with the easy annuity functions of the calculator?

I know that you can't solve for i on the calculator (unless mine is just broken).....normally when there is something to solve for i, it is done with the quadratic formula or some other method of manipulating and cancelling so it's good to know annuity formulas. If you know one it is easy to find a formula for all the others if you know the principles well.

Double Down Trent
08-21-2002, 02:40 PM
There are plenty of interest theory problems where the calculator is useless. All of the algebraic questions with no numbers comes to mind. You know:

Which of the following are correct:

A) I Only B) II Only C) I &amp; III D) II &amp; III E) None of A, B, C, or D

Double Down Trent
08-21-2002, 02:43 PM
C2 Taker:

Your calculator must be broken. The BA-35 Solar can calculate i. There are some instnaces where it cannot, but they are usually pretty rare. As Long as you know the values for four of the variables(n,i,PV,PMT,FV), the fifth can almost always be calculated by the calculator.

bg23516
08-21-2002, 03:26 PM
BB is right that the calculator can solve for i, if you use it correctly. That's what I meant when I said to learn to use it and the principles. The calculator can do much more than it seems.

As for the questions you mentioned that are purely algebraic, those are fairly rare nowadays. I don't remember seeing all that many (1 or 2 per, at most) in recent exams. I still recommend learning many of the formulas... it often can help you condense problems.

c3 taker
08-21-2002, 04:22 PM
it's pretty strange acutally....I'll type in n, pv, pmt, and fv and then click compute i and the screen goes blank. I'll have to look into that. Usually solving for i is the hardest b/c there are multiple i's in most of them and the algebra is usually the most difficult

bg23516
08-21-2002, 04:25 PM
You may need to wait up to 30 seconds (or more) for the result. It says something to that effect in the manual. Give it time.

drctypea
08-21-2002, 05:05 PM
make sure you put the FV in as a neg number...im not playing with the calc now but i remember i had a similar problem and i think it was because of the reason i just mentioned. try it..hope it helps..