Comments on: The Interest Rates of Loving A Sexy Maths Tutor http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor Sassy O Level Maths Tuition, Questions & Tips from Singapore's Favourite Private Tutor Sun, 05 Feb 2012 17:08:39 +0000 hourly 1 By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9964 Miss Loi Thu, 26 Jun 2008 05:06:09 +0000 http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9964 Haha <b>Li-sa</b> as you probably know Miss Loi has been pretty <a href="/miss-loi-the-tutor/miss-loi-is-sunday-times-cover-girl" rel="nofollow">overwhelmed</a> for the past week and so she only has time to 'sneak' in a reply or two each night to the questions that you did :) But now that the dust has somewhat settled, think it's time to start blogging again - Miss Loi misses this place! *embraces computer screen* Haha Li-sa as you probably know Miss Loi has been pretty overwhelmed for the past week and so she only has time to 'sneak' in a reply or two each night to the questions that you did :)

But now that the dust has somewhat settled, think it's time to start blogging again - Miss Loi misses this place! *embraces computer screen*

]]> By: Li-sa http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9962 Li-sa Thu, 26 Jun 2008 04:49:52 +0000 http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9962 The EAR and APR stuff came from the notes the math panel teacher gave me. I just didn't want to make the whole thing so complicated so I summed it up. And I will be shutting down my old blog soon so just call me Li-sa, my actual cyber-name. You can find me in squareCircleZ; it's the same person. My teacher also dares to write comments boldly. Once I did my work very messily and she wrote on a separate page forcefully (poor paper...I love paper): "IF YOU DON'T TIDY UP YOUR WORK, I WON'T MARK YOUR EXERCISE BOOK ANYMORE." I was so afraid I succumbed to writing *nicely*. It's okay to comment fearlessly; it shows you are brave enough to save, like superheroes. Do they tiptoe into castles and rescue damsels in distress? Hardly ever. Just call me Li-sa. The EAR and APR stuff came from the notes the math panel teacher gave me. I just didn't want to make the whole thing so complicated so I summed it up. And I will be shutting down my old blog soon so just call me Li-sa, my actual cyber-name. You can find me in squareCircleZ; it's the same person.

My teacher also dares to write comments boldly. Once I did my work very messily and she wrote on a separate page forcefully (poor paper...I love paper): "IF YOU DON'T TIDY UP YOUR WORK, I WON'T MARK YOUR EXERCISE BOOK ANYMORE." I was so afraid I succumbed to writing *nicely*. It's okay to comment fearlessly; it shows you are brave enough to save, like superheroes. Do they tiptoe into castles and rescue damsels in distress? Hardly ever.

Just call me Li-sa.

]]> By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9957 Miss Loi Thu, 26 Jun 2008 04:24:56 +0000 http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9957 *Struts boldly in to comment on <b>fggffggf</b>'s solution - since she's already been caught by <b>fggffggf</b> sneaking in quietly* In any case, may this example demonstrate to all the potentially snowballing effect of a 'low' quoted interested rate (monthly? daily? hourly?) over a extended period of time <var>T</var>. Woe to the <del>大耳窿s</del> <del>banks</del> <del>大耳窿s</del> <del>banks</del> 大耳窿s! *getting confused* :P *Struts boldly in to comment on fggffggf's solution - since she's already been caught by fggffggf sneaking in quietly*

In any case, may this example demonstrate to all the potentially snowballing effect of a 'low' quoted interested rate (monthly? daily? hourly?) over a extended period of time T.

Woe to the 大耳窿s banks 大耳窿s banks 大耳窿s! *getting confused* :P

]]> By: fggffggf http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9726 fggffggf Wed, 18 Jun 2008 06:14:02 +0000 http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9726 For 1. <b>iff p.a. = per integral year</b> total amount to pay ($) = [pmath]12000(1+300%*4) = 156000[/pmath] <b>iff p.a. = per non-integral year</b> total amount to pay ($) = [pmath]12000(1+300%(4+6/12)) = 174000[/pmath] <div class="highlight"> Nice of you to add the calculation based on per integral year (which simply entails <em>rounding down</em> to the nearest whole year when calculating the interest). Banks would love to use this method when calculating the interest owed to you as they will save a tidy sum should you withdraw your money before the year is up! HOWEVER in the context of general O-Level questions, calculations should be done as per non-integral year as detailed by you above (so the answer is a total $174000 owed in 4 yrs 6 mths' time based on simple interest). The loanshark wouldn't be so stupid to throw away 6 months' worth of interest away! <strong>POTENTIAL CARELESS MISTAKE:</strong> Many students are so used to the simple interest formula <m>I = PRT/100</m> appearing in textbooks everywhere that they sometimes forget to add the <em>principal</em> some of $12000 to their final answer! </div> For 2. total amount to pay ($) = [pmath] 12000(1+{60%}/12)^(4*12+6) = 167264.3533[/pmath] (cor. to 4 d.p.) <div class="highlight"> Yes, the usual practice in the exam when you encounter interest that's compounded <em>monthly</em> is to simply divide the yearly interest rate (60% in this case) by 12 months, and make sure your Time <var>T</var> is now in <em>months</em>. <strong>POTENTIAL CARELESS MISTAKE (again):</strong> This time the compound interest formula <m>A = P(1+{R/100})^T</m> appearing in textbooks everywhere <em>already</em> takes into account the principal sum. So you DO NOT have to add $12000 to your final answer (which is $167264.35 as worked out above)! What a way for textbooks to confuse our poor students huh? :? </div> <i><a href="http://mathworld.wolfram.com/Iff.html" rel="nofollow">iff = if and only if.</a></i> .'. iff p.a.=per integral year: simple interest else: compound interest As I thought that well, loan sharks suck as much money as possible, I included both even though only one could be chosen in the public exam. <span class="highlight">One again in the context of the exam questions, compound interest is the way to go ($167264.35 vs $174000) for the <i>Ah Beng</i>. But seriously he should just forget about the whole idea and go learn some financial planning instead :P</span> Ah and one more thing: Some time ago at my school (not in Singapore, so just for interest), I attended a math activity on loans by loan sharks: Effective Interest Rate: [pmath](1+r)^f-1[/pmath] where r = interest rate for a single period, f = frequency of compounding, i.e. the number of years [pmath]*[/pmath] the number of compounding periods per year For instance, what is the EIR for 12% compounded quarterly? Answer: Stated interest is 12%; [pmath]r = {12%}/4[/pmath] quarters = 3% per quarter f = 4 (i.e. quarterly) Effective rate = [pmath](1+0.03)^4-1 = 0.1255[/pmath] .'. effective rate = 12.55% The loan sharks love this:[no wonder they're called 大耳窿 (lit. big EAR holes) '.' got so many bucks and pierced big EAR holes] Effective Annual rates (EARs) [pmath](1+(quoted rate)/m)^m-1[/pmath] where m = number of periods per year. APR: annual percentage rate, the “total” rate per year. Case in point: A bank charges 1% per month on a certain loan. Find the APR and EAR. Answer: APR=[pmath]1%*12=12%[/pmath] EAR=[pmath](1+{12%}/12)^12-1=1.126825-1=12.6825%[/pmath] Then this year the bank changes the terms: on agreeing to the loan, one gets $1,000 instant credit; the bank claims, "12% simple interest! 3 years to pay! Low, low monthly payment!" How much will the debtor owe at the end of the 3 years and is it really a 12%-simple-interest-based loan? The debtor owes [pmath]$1000 + $1000(0.12)(3) = $1360[/pmath] Each month the debtor must pay [pmath]{$1360}/36 = $37.78[/pmath] (yes, these money suckers love rounding everything UP.) Is this a 12% loan? Let's see: [pmath]1000 = 37.78*{(1-1/(1+r)^36)}{1/r}[/pmath] <span class="highlight">This is the step that transforms the innocent-looking interest rate into a astronomical 天文数字 effective rate. Care to elaborate how you derived this?</span> [pmath]r = 1.767%[/pmath]per month APR = [pmath]12(1.767%)=21.204%[/pmath] EAR = [pmath](1+1.767%)^12 - 1[/pmath] [pmath]{} =1.01767^12 - 1=23.39%[/pmath]哗！天文数字！Poor dude. But limit of EAR is [pmath]e^q-1[/pmath] where q is the quoted rate; e: base of the natural log. For 1. iff p.a. = per integral year
total amount to pay ($) = 12000(1+300%*4) = 156000
iff p.a. = per non-integral year
total amount to pay ($) = 12000(1+300%(4+6/12)) = 174000

Nice of you to add the calculation based on per integral year (which simply entails rounding down to the nearest whole year when calculating the interest). Banks would love to use this method when calculating the interest owed to you as they will save a tidy sum should you withdraw your money before the year is up!

HOWEVER in the context of general O-Level questions, calculations should be done as per non-integral year as detailed by you above (so the answer is a total $174000 owed in 4 yrs 6 mths' time based on simple interest). The loanshark wouldn't be so stupid to throw away 6 months' worth of interest away!

POTENTIAL CARELESS MISTAKE: Many students are so used to the simple interest formula I = PRT/100 appearing in textbooks everywhere that they sometimes forget to add the principal some of $12000 to their final answer!

For 2. total amount to pay ($) = 12000(1+{60%}/12)^(4*12+6) = 167264.3533 (cor. to 4 d.p.)

Yes, the usual practice in the exam when you encounter interest that's compounded monthly is to simply divide the yearly interest rate (60% in this case) by 12 months, and make sure your Time T is now in months.

POTENTIAL CARELESS MISTAKE (again): This time the compound interest formula A = P(1+{R/100})^T appearing in textbooks everywhere already takes into account the principal sum. So you DO NOT have to add $12000 to your final answer (which is $167264.35 as worked out above)! What a way for textbooks to confuse our poor students huh? :?

iff = if and only if.
.'. iff p.a.=per integral year: simple interest
else: compound interest
As I thought that well, loan sharks suck as much money as possible, I included both even though only one could be chosen in the public exam.

One again in the context of the exam questions, compound interest is the way to go ($167264.35 vs $174000) for the Ah Beng. But seriously he should just forget about the whole idea and go learn some financial planning instead :P

Ah and one more thing: Some time ago at my school (not in Singapore, so just for interest), I attended a math activity on loans by loan sharks:

Effective Interest Rate: (1+r)^f-1
where
r = interest rate for a single period,
f = frequency of compounding, i.e. the number of years * the number of compounding periods per year

For instance, what is the EIR for 12% compounded quarterly?

Answer:
Stated interest is 12%;
r = {12%}/4 quarters = 3% per quarter
f = 4 (i.e. quarterly)
Effective rate = (1+0.03)^4-1 = 0.1255
.'. effective rate = 12.55%

The loan sharks love this:[no wonder they're called 大耳窿 (lit. big EAR holes) '.' got so many bucks and pierced big EAR holes]

Effective Annual rates (EARs) (1+(quoted rate)/m)^m-1 where m = number of periods per year.
APR: annual percentage rate, the “total” rate per year.

Case in point: A bank charges 1% per month on a certain loan. Find the APR and EAR.

Answer:
APR=1%*12=12%
EAR=(1+{12%}/12)^12-1=1.126825-1=12.6825%

Then this year the bank changes the terms: on agreeing to the loan, one gets $1,000 instant credit; the bank claims, "12% simple interest! 3 years to pay! Low, low monthly payment!" How much will the debtor owe at the end of the 3 years and is it really a 12%-simple-interest-based loan?

The debtor owes $1000 + $1000(0.12)(3) = $1360
Each month the debtor must pay {$1360}/36 = $37.78 (yes, these money suckers love rounding everything UP.)

Is this a 12% loan? Let's see:
1000 = 37.78*{(1-1/(1+r)^36)}{1/r}

This is the step that transforms the innocent-looking interest rate into a astronomical 天文数字 effective rate. Care to elaborate how you derived this?

r = 1.767%per month
APR = 12(1.767%)=21.204%
EAR = (1+1.767%)^12 - 1
{} =1.01767^12 - 1=23.39%哗！天文数字！Poor dude.

But limit of EAR is e^q-1 where q is the quoted rate; e: base of the natural log.

]]> By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9440 Miss Loi Tue, 10 Jun 2008 15:59:55 +0000 http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9440 Hello <b>jr</b>. Care to show how you found that compound is the better option? The difference between the two should be pretty close ;) <b>TOH KIAT SHENG KEN:</b> If you can solve this sad, sad question, you'd discover that either way the poor <i>Ah Beng</i> will have no money left for <i>rokok</i>. Hello jr. Care to show how you found that compound is the better option? The difference between the two should be pretty close ;)

TOH KIAT SHENG KEN: If you can solve this sad, sad question, you'd discover that either way the poor Ah Beng will have no money left for rokok.

]]> By: tohkiatshengKEN http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9435 tohkiatshengKEN Tue, 10 Jun 2008 14:47:35 +0000 http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9435 wow! sup rokok! (: wow! sup rokok! (:

]]> By: jr http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9415 jr Mon, 09 Jun 2008 19:22:53 +0000 http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-9415 poor ah beng. missed his lesson. compound is better rite? poor ah beng. missed his lesson.
compound is better rite?

]]> By: Kiroiitsuki http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-4385 Kiroiitsuki Sun, 24 Feb 2008 15:32:20 +0000 http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-4385 Well well...LOL "unlikely of circumstances" ? Thats kinda perverse if you ask me lolz i thought girls in contemporary like to be pragmatic - "no $ no honey" Well well...LOL "unlikely of circumstances" ? Thats kinda perverse if you ask me lolz i thought girls in contemporary like to be pragmatic - "no $ no honey"

]]> By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-4383 Miss Loi Sun, 24 Feb 2008 14:53:42 +0000 http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-4383 <b>Kiroii</b>, yeah it's a little tragic but lurve always happens in the most unlikely of circumstances. Moreover, if you've read through <a href="/miss-loi-the-tutor/what-happened-last-night" rel="nofollow">this tag</a>, you'll know that Care Bears will never make it into Miss Loi's agenda ;) Kiroii, yeah it's a little tragic but lurve always happens in the most unlikely of circumstances. Moreover, if you've read through this tag, you'll know that Care Bears will never make it into Miss Loi's agenda ;)

]]> By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-4381 Miss Loi Sun, 24 Feb 2008 14:47:08 +0000 http://www.exampaper.com.sg/questions/e-maths/the-interest-rates-of-loving-a-sexy-maths-tutor#comment-4381 Hello <b>Cendrine</b>! Mother and daughter not yet, but <a href="/questions/a-maths/one-trigonometry-question-to-get-into-jc" rel="nofollow">father and son</a> are screening now :D Hello Cendrine! Mother and daughter not yet, but father and son are screening now :D

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