Loan Repayment/Annuties (2 Viewers)

[Sy123]

Doing 2U trials and the HSCs, I sometimes lose marks over the annuity and loan repayment questions (the more complex ones). I usually lose marks because I miscount the number of times interest is added and such and it frustrates me quite a bit.

So I am going to ask, how do people approach these types of questions? Do you do anything specific, count the amount of years etc etc.

Id hate to lose my only marks to this section as I have before.

 

[Jashua_Long]

Doing 2U trials and the HSCs, I sometimes lose marks over the annuity and loan repayment questions (the more complex ones). I usually lose marks because I miscount the number of times interest is added and such and it frustrates me quite a bit.

So I am going to ask, how do people approach these types of questions? Do you do anything specific, count the amount of years etc etc.

Id hate to lose my only marks to this section as I have before.

Look at the base case.

Take an example.

A person takes out a loan of $500 000, interest =6% p.a., They make monthly repayments M. Find a formula for a An (The amount owing after n repayments).

r = 6% / 12 = 0.005

A1 = 500000(1.005) -M

A2 = [500000(1.005) -M](1.005) - M

A2 = 500000(1.005)^2 -M(1+1.005)

Note: A2 has two terms in the final bracket 9and the final term has a power of 1, i.e. (2-1) . Therefore, An must have n terms in the final bracket, and the final term has power (n-1)

An = 500000*1.005^n -M (1+1.005 + 1.005^2 + .....+ 1.005^(n-1) )

etc. sum the GP

 

[Jashua_Long]

If that is not what you meant then post up an example question that you got wrong and people can tell you how they approach it .

 

[Sy123]

Well I have problems in general with finding the amount of things such as number of years/interest etc. I got a question wrong in my CSSA trial but I cant find it so I cant post it, but I got this question 'wrong' from HSC 2004

Part iii, I know exactly how to do everything, the problem is they count t=13, while I counted t=14 (I counted it with my fingers to be sure too and it should definitely be t=14). I want to know what is wrong with my thinking or if the board of studies were wrong (unlikely)

Another technicality question:










The problem is I disgregarded theta=0 since I assumed that it cant be a limiting sum if its 0. Or can it?

 

[Jashua_Long]

Note the word "beginning".

The beginning of 2004 is equivalent to the end of 2003


Then you can do the standard, n= (2003 - 1991) +1

 

[Sy123]

Note the word "beginning".

Oh I see what I did, when I counted on my fingers from 1991, I started with t=1 instead of t=0

I read this good 'formula' for counting:



The number of terms are p-q+1

Does this work with EVERYthing that I have to count such as years, number of times interest is added etc.?

 

[RishBonjour]

I have the EXACT same problem.
some of them are very vague. especially when they ask to change in midway, not sure to add interest before or after.
But depends on the question.
I tend to draw a number line on the top. starting with year 1 etc and n = whatever. just to keep track.

 

[Jashua_Long]

Well I have problems in general with finding the amount of things such as number of years/interest etc. I got a question wrong in my CSSA trial but I cant find it so I cant post it, but I got this question 'wrong' from HSC 2004

Part iii, I know exactly how to do everything, the problem is they count t=13, while I counted t=14 (I counted it with my fingers to be sure too and it should definitely be t=14). I want to know what is wrong with my thinking or if the board of studies were wrong (unlikely)

Another technicality question:










The problem is I disgregarded theta=0 since I assumed that it cant be a limiting sum if its 0. Or can it?

If theta =0, r=0. Condition for limiting sum |r|<1.

|0| is less than 1.

 

[Sy123]

I have the EXACT same problem.
some of them are very vague. especially when they ask to change in midway, not sure to add interest before or after.
But depends on the question.
I tend to draw a number line on the top. starting with year 1 etc and n = whatever. just to keep track.

Yeah that happens to me with the ambiguous wording of the annuity questions :/
Sometimes I cant tell whether A_1= 1000 or A_1=1000(interest)

Good idea with the number line though

 

[Sy123]

If theta =0, r=0. Condition for limitting sum |r|<1.

|0| is less than 1.

The only reason why that condition is given is because it makes the series converge to something.

In the case of 0 however it just well, stays put it doesnt do anything, so I assumed that it isnt a limiting sum

 

[RishBonjour]

I've gone through a few past papers today (just looking over and doing those that look interesting) and i KEEP getting interest ones wrong. would we get like 2/3 if everything else is right but the interest?

 

[barbernator]

yep its a limiting sum if theta=0. any number that gives the series a finite value can be considered a limiting sum.

 

[Sy123]

Alright then lol.

I will see if I can post the interest question that I got wrong.

 

[barbernator]

Alright then lol.

I will see if I can post the interest question that I got wrong.

yeh go for it

 

[Capt Rifle]

Yeh this topic of ap and gp is freakin annoying....

 

[Keelan134]

Beginning and at the end of the year questions are a pain, but just work out the first year to get a feel for it,

A fisherman has 100000 fish in January 2000 and over the course of the year the population increases by 10%. In December 2000 he sells 15400 fish to a retailer at $10/unit.
i) How many fish are there in December 2001 before the purchase by the retailer?
(100000*1.1 -15400) * 1.1 = Whatever....

Also look out for questions where there are interest free periods and compounding annually but only yearly installments, e.g.
Keelan gets a $100 loan, interest rate of 48% p.a. compounding monthly. Keelan repays this debt in annual installments over the course of 50 years. Determine his annual installment.

100*1.4^600 - Y((1.4^50)^12 - 1)
________________
(1.4^50) -1

etc etc

 

[Keelan134]

I've gone through a few past papers today (just looking over and doing those that look interesting) and i KEEP getting interest ones wrong. would we get like 2/3 if everything else is right but the interest?

Typically they have a few parts to them, with the first question being prove the formula to calculate his amount owing etc. Then if you cant get to the formula they want, just use the formula provided for the other questions.

But yeah I looked at the marking criteria for the interest rate questions from my school's trials and half yearlys and they're typically a mark for the answer, a mark for getting M or n by itself, and another for setting it up in the right formula i.e P*1+r - M(r^n-1 / r-1)

 

[Capt Rifle]

how can I get better at these questions? I don't want them to stuff me up in the future....

 

[osak23]

do you have any harder examples to post up

like the change in the interest rate in the middle

 

[Keelan134]

do you have any harder examples to post up

like the change in the interest rate in the middle

Despite it taking Keelan 50 years to pay off his $100 loan, he goes to Harvey Norman to buy a high end TV despite the warning of the issues with Interest free periods from his favourite television show, Today Tonight, of which he somehow watches without a tv. He chooses the $5000 TV, and will pay the tv off monthly over 5 years, at an interest rate of 12%p.a. compounding monthly. His first 3 months are free from interest, however he must still make monthly repayments.
i) Determine how much Price remains after the 3 months interest free in terms of M

ii) Determine the formula for Price remaining (P) for n months.

iii) Find the value of M