Question 8)c)i help anyone? (1 Viewer)

[Perfect Element]

Hey guys, just got a question about 8)c)i

Anyone able to show me how to do it?

Ignoring formulas and just working off logic I ended up with this:


A2 = (3,000,000 - 480,000) x 1.12 - 480,000

= (3x10^6)(1.12) - (4.8x10^5)(1+1.12)

3,000,000 payed at the start of 2005, at the end of 2005 they repay 480,000. The balance then gets interest of 12% at the start of 2006. At the end of 2006 they repay a further 480,000. Hence, the amount owing after the second repayment is what I wrote isn't it?

So where does the extra factor of 1.12 in the first term come from?

Surely they don't add a year's interest onto the 3,000,000 as soon as it's borrowed!?

 

[Ultraviolent]

The deer is teal

 

[Bookie]

It becomes part of a GP.

3 x 10^6 x 1.12^n - [(4.8 x 10^5) / 0.12](1.12^n-1)

take the 1000000 out.

10^6 (3(1.12^n) - 4(1.12^n) - 4)
(10^6)(1.12^n)(3 - 4) + 4
10^6 (4 - 1.12^n)

Kapish?

 

[seremify007]

A2 = (3,000,000 - 480,000) x 1.12 - 480,000

= (3x10^6)(1.12) - (4.8x10^5)(1+1.12)

Try going from A1- it makes more sense.

A1 = (3 * 10^6)(1.12) - (4.8 * 10^5)

A2 = A1 * 1.12 - (4.8 * 10^5)
= ((3 * 10^6)(1.12) - (4.8 * 10^5))(1.12) - (4.8 * 10^5)
= (3 * 10^6)(1.12)^2 - (4.8 * 10^5)(1.12) - (4.8 * 10^5)
= (3 * 10^6)(1.12)^2 - (4.8 * 10^5)(1 + 1.12)

... That (1 + 1.12) bit becomes a GP later on where you just use the (ar^(n-1))/(r-1) in part (ii) to get the An - as Bookie said. Hope this helps =]

 

[Perfect Element]

It becomes part of a GP.

3 x 10^6 x 1.12^n - [(4.8 x 10^5) / 0.12](1.12^n-1)

take the 1000000 out.

10^6 (3(1.12^n) - 4(1.12^n) - 4)
(10^6)(1.12^n)(3 - 4) + 4
10^6 (4 - 1.12^n)

Kapish?

I'm asking about Question c)i not c)ii.

 

[Perfect Element]

Try going from A1- it makes more sense.

A1 = (3 * 10^6)(1.12) - (4.8 * 10^5)

A2 = A1 * 1.12 - (4.8 * 10^5)
= ((3 * 10^6)(1.12) - (4.8 * 10^5))(1.12) - (4.8 * 10^5)
= (3 * 10^6)(1.12)^2 - (4.8 * 10^5)(1.12) - (4.8 * 10^5)
= (3 * 10^6)(1.12)^2 - (4.8 * 10^5)(1 + 1.12)

... That (1 + 1.12) bit becomes a GP later on where you just use the (ar^(n-1))/(r-1) in part (ii) to get the An - as Bookie said. Hope this helps =]

See I don't think your A1 is correct.

The question states, the "first repayment being made at the end of 2005". The interest isn't calculated until "the beginning of the year".

Therefore the first repayment is at the end of the first year, and the first interest is at the start of the second year.

A1 means the balance owing after the first repayment.

There is no interest added between the time of the initial borrowing and the first repayment.

Hence

A1 = 3,000,000 - 480,000

Which is at the end of 2005

THEN at the start of 2006 the interest is added. See what I'm saying?

 

[Perfect Element]

edit: very poorly worded exam question + exam stress = misinterpretation of question.

Move along, nothing to see here.



(The question should have stated "At the end of the year, interest is calculated on what the balance was at the beginning of the year" to make it more clear. Saying the "interest was calculated on the balance at the beginning of the year" could mean either "at the beginning of the year the interest was calculated on the balance" as I interpreted it, or "interest was calculated on what the balance was at the beginning of the year".)

 

[seremify007]

I'm only used to it because in a few past papers they had poorly worded questions. But I see your point, although it makes sense that there's interest charged on the loan immediately after it is arranged- I know this isn't the case with credit-cards and int-free periods, but it seems to make sense to me.

Eg. If you borrow $10,000 to buy a car- they add the interest on top of that loan to the amount owing immediately- why would they wait until you made the first repayment?

 

[filo_romz]

hey guys .. i had some confusion with that question too .. i put 2018 .. >< coz like after 2017, they still owe some bit of money left and they needed to repay that the year after .. so i rounded up .. =/ is that right? ><" all my friends reckon its 2017 .. kinda felt nigelated .. -_-''

 

[SoulSearcher]

i wouldnt have a clue

got 2017 like those guys

 

[webby234]

I got 12. something as the term, which rounds up to the 13th year.

Year 1 - 2005
2 - 2006
12 - 2016
13 - 2017

so the loan will be paid off in 2017