TI BA2 Calculator - Calculating Annuity Variables

[ajhardy]

Been looking at using my calculator more extensively and looking at using the TVM functions. Using the calculator effectively should speed up the calculation steps. However, I'm having some problems with calculating some of the variables of annuities when payments are made more than once per period.

As an example question:

An annuity costs £6000 to receive the amount of £1000 per year, paid quarterly in arrears for the next 10 years. What effective rate of interest makes this a fair sale price?

I can calculate this with the calculator using 40 periods with a payment of £250 per period and then adjust the quarterly interest rate to get an annual interest rate, but I've not been able to get the answer using 10 periods with 4payments per year.

For the answer, using N = 40, PV = 6000, PMT = -250, FV = 0 and then [CPT] [I/Y] you get 2.77% which is then adjusted to an annual rate giving 11.55%.

I've tried to use the same, but with PMT = -1000, N = 10 and P/Y = 4 (reached by [2ND] [P/Y]) and I get an answer of 42.23% so obviously I'm typing something wrong into the calculator. I've looked up various tutorials on the TI BA2 Plus but none of them seem to address how to deal with an annuity that is paid more frequently than once per year.

Any other TI BA2 Plus users out there that know the answer to this (or the button strokes) would be great.

[Obviously I could calculate the number from first principles but the point is that I want to use the calculator so there is no need to explain to me how to calculate it manually...]

 

[Mark Mitchell]

All I can suggest is to set:

P/Y = 4 (check using the down arrow that C/Y=1)
FV = 0
PV = 6000
PMT = -250
N = 40

This gives the answer of 11.5477% straightaway.

I can't find a better way, in particular one where you don't need to convert to the quarterly payment and the number of quarterly payments.

From my manual, it looks like the calculator doesn't do what you're hoping it will!

 

[ajhardy]

Mark,

Thanks for that. I agree that the secret is in the [C/Y] setting.

Another, similarish question I have is to do with loan amortisation schedules and using the AMORT spreadsheet function.

If I have this problem:

£10,000 loan, 3% nominal interest rate compounding monthly, monthly payments over 5 years.

Comparing my calculator values...
Using the TVM buttons:
N = 60
I/Y = 3%
P/Y = C/Y = 12
PV = 100000

Then, [CPT] [PMT] I get payment - £1796.87 (which agrees with my hand calcs)

To look at the loan outstanding after month 10, using [2ND] [AMORT], with P1 = P2 = 10, I get BAL = £84,356.12 (which agrees with my hand calcs)

Looking at the interest paid over months 15 - 25, I have some problems though...

Using P1 = 15 and P2 = 25, I get:
BAL = 60,145.58 (agrees with hand calcs)
PRN = -17,842.80 (doesn't agree)
INT = -1,922.77 (doesn't agree)

but...when calculating by hand I get the principle repaid over the same months (1796.87 * [a45@0.25% - a35@0.25%]) to be £16,240.91 with interest repaid of £1,727.79 (£1796.87 * 10 - 16240.91).

At P1 = P2 = 15, I get BAL = £76,386.48 (agrees with hand calcs), so, I'm not sure what is going wrong here as the balance calculated by the amortisation schedule is correct, but the principle and interest payments are not right....any thoughts?

 

[Mark Mitchell]

When you use P1 = 15 and P2 = 25, the calculator returns:

- the balance outstanding after the 25th payment
- the principal repaid in the 15th to 25th payments inclusive (that's 11 payments in total)
- the interest paid in the 15th to 25th payments inclusive (again 11 payments in total)

To match your numbers you need P1 = 16 and P2 = 25.

 

[Hobbs]

Out of curiosity, do many people use these built-in calculator functions in exams?

I kind of like to keep myself thinking through the calculation, hopefully catching anything stupid in my setup of the calc.

Maybe I'm just paranoid.

 

[Mark Mitchell]

From what I see in tutorials, most students seem to use a Casio fx-85 of some description, which doesn't have these finanical features.

 

[Hobbs]

From what I see in tutorials, most students seem to use a Casio fx-85 of some description, which doesn't have these finanical features.

This interests me. After the hastly aborted attempt to ban the hp12c a few years ago, I had assumed that there was a strong majority of users interested in using the best calculator.

I guess they just have powerful friends.

 

[antzlck]

Would you get penalised for using the calculator to work some of these problems? More specifically, would not showing your working (if you're not doing it manually there's no point in writing out the equations) be penalised? As financial calculators are allowed in the exam I'm hoping you wouldn't be penalised for actually using them!

 

[Tim.Sullivan]

You won't get penalised for using the calculator and simply stating the result - unless of course the question asks you to show your workings.

But if you make a mistake your result will be wrong and you'll get zero marks for that result. If you were to do the calcs manually and wrote the steps involved as well as the result....but made a small error within the steps...you might still get some marks. Especially if the examiner can see that overall you understood the question and the formula required, made a minor error on only one step and can see that the rest were followed through correctly.

I was using the BA2 for my first few exams and then changed to the fx-85. When I wrote CT1 I preferred not to rely on the BA2's annuity and amortisation functions so simply didn't use them. I personally much prefer the fx-85 for two main reasons: a) it produces results as a formula similarly to how you see them in the CT1 notes and exam papers. For example 2.35*5 = 11.75 but the fx-85 also gives this as 47/4. And b) the stats mode on the fx-85 allows you to easily do interpolation; very useful for the standard-normal distribution probability q's in CT1 and significantly more so in CT3. Just my thoughts!

Tim

 

[antzlck]

You won't get penalised for using the calculator and simply stating the result - unless of course the question asks you to show your workings.

But if you make a mistake your result will be wrong and you'll get zero marks for that result. If you were to do the calcs manually and wrote the steps involved as well as the result....but made a small error within the steps...you might still get some marks. Especially if the examiner can see that overall you understood the question and the formula required, made a minor error on only one step and can see that the rest were followed through correctly.

I was using the BA2 for my first few exams and then changed to the fx-85. When I wrote CT1 I preferred not to rely on the BA2's annuity and amortisation functions so simply didn't use them. I personally much prefer the fx-85 for two main reasons: a) it produces results as a formula similarly to how you see them in the CT1 notes and exam papers. For example 2.35*5 = 11.75 but the fx-85 also gives this as 47/4. And b) the stats mode on the fx-85 allows you to easily do interpolation; very useful for the standard-normal distribution probability q's in CT1 and significantly more so in CT3. Just my thoughts!

Tim

Should have thanked you months ago! I used both calculators in the exam today. Mainly the Casio but the BAII definitely came in handy to quickly find an interest rate or convert between effective and nominal rates quickly where this is an intermediate step and not the final answer to the question. When using it to solve i I did first write out the EOV and also checked my answer afterwards.