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

]]>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.

]]>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* 😛

total amount to pay ($) =

total amount to pay ($) =

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 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 ($) = (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 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 😛

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:

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%;

quarters = 3% per quarter

f = 4 (i.e. quarterly)

Effective rate =

.'. 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) 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=

EAR=

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

Each month the debtor must pay (yes, these money suckers love rounding everything UP.)

Is this a 12% loan? Let's see:

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?

per month

APR =

EAR =

哗！天文数字！Poor dude.

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

]]>**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*.

compound is better rite? ]]>