Loan repayments (2 Viewers)

[MrBrightside]

ok this is weird, I don't know it the book is wrong or if its me (probably is me).

View attachment 22442

my ans was $42 028.80

 

[hscmathstutor10]

lol i thought today was a school day

 

[MrBrightside]

me to ^^

 

[hscmathstutor10]

so he pays 5% straight away , so he has 0.95 x 35000 left to pay = 33250 nd ill call this P to make the work easiesr, and let R be the repayment

now the rate = 12%pa= 1%/month = 0.01/month

and A= P ( 1+R)^n

now let A (n) be the amount owing after n months

so A (1) = P ( 1.01) -R { he is charged interest then makes a payment }

A (2) = [ P (1.01) -R] (1.01) -R { same idea as above}
A (2) = P (1.01)^2 -R - R(1.01)
A (2) = P ( 1.01)^2 -R (1+1.01) { pattern is easy to see, in the last bracket we will have n terms, with the nth term having a power of n-1 }

so A (n) = P (1.01)^n - R ( 1+1.01 + 1.01^2 +.... 1.01^(n-1) )

now apply the sum of a GP formula to last part, with a=1, r=1.01, n=n

A (n) = P (1.01)^n -R [ 1 ( 1-(1.01)^n ) / (1-1.01) ]

A (n) = P (1.01)^n +100R [ 1- (1.01)^n]

now in 4yrs ( 48months , he owes nothin)

A ( 48) = 0

so P(1.01)^48 + 100R [ 1- (1.01)^48] =0
now solve for R

100R [ 1 -(1.01)^48] = - P ( 1.01)^48
100R= -P(1.01)^48 / [ ( 1-(1.01)^48 ]
R = -P ( 1.01)^48 / [ 100 ( 1-(1.01)^48 ) ]

and sub in P

R= $ 875.60

now he paided this 48 times

so he ends up paying $875.60 x 48 =$42 028.80

hmm not quite, you have fallen into the trap.

remember, we have ignored for the moment the 5% that paided as the desposit,

add this 5% on ie 0.05 x 35000 = $1750

so final answer = 1750 + 42 028. 80 and the book is correct

 

[MrBrightside]

so he pays 5% straight away , so he has 0.95 x 35000 left to pay = 33250 nd ill call this P to make the work easiesr, and let R be the repayment

now the rate = 12%pa= 1%/month = 0.01/month

and A= P ( 1+R)^n

now let A (n) be the amount owing after n months

so A (1) = P ( 1.01) -R { he is charged interest then makes a payment }

A (2) = [ P (1.01) -R] (1.01) -R { same idea as above}
A (2) = P (1.01)^2 -R - R(1.01)
A (2) = P ( 1.01)^2 -R (1+1.01) { pattern is easy to see, in the last bracket we will have n terms, with the nth term having a power of n-1 }

so A (n) = P (1.01)^n - R ( 1+1.01 + 1.01^2 +.... 1.01^(n-1) )

now apply the sum of a GP formula to last part, with a=1, r=1.01, n=n

A (n) = P (1.01)^n -R [ 1 ( 1-(1.01)^n ) / (1-1.01) ]

A (n) = P (1.01)^n +100R [ 1- (1.01)^n]

now in 4yrs ( 48months , he owes nothin)

A ( 48) = 0

so P(1.01)^48 + 100R [ 1- (1.01)^48] =0
now solve for R

100R [ 1 -(1.01)^48] = - P ( 1.01)^48
100R= -P(1.01)^48 / [ ( 1-(1.01)^48 ]
R = -P ( 1.01)^48 / [ 100 ( 1-(1.01)^48 ) ]

and sub in P

R= $ 875.60

now he paided this 48 times

so he ends up paying $875.60 x 48 =$42 028.80

hmm not quite, you have fallen into the trap.

remember, we have ignored for the moment the 5% that paided as the desposit,

add this 5% on ie 0.05 x 35000 = $1750

so final answer = 1750 + 42 028. 80 and the book is correct

oooo WTF, how was i meant to know that the deposit gets included. omg.

btw at the start I deducted the deposit from P so 35000 - 1750. is that correct?

btw y do you use capital R? i've never seen it used.

 

[hscmathstutor10]

oooo WTF, how was i meant to know that the deposit gets included. omg.

btw at the start I deducted the deposit from P so 35000 - 1750. is that correct?

btw y do you use capital R? i've never seen it used.

I have some serious doubts in your math teacher's ability if he hasnt done that yet, it is always convention to use R to mean repayment in finance questions.

Man I should be a maths teacher, I have only just finished first year uni but I reckon I would be better than atleast 50% of them out there

 

[MrBrightside]

I have some serious doubts in your math teacher's ability if he hasnt done that yet, it is always convention to use R to mean repayment in finance questions.

Man I should be a maths teacher, I have only just finished first year uni but I reckon I would be better than atleast 50% of them out there

Iv'e be taught to use capital M.....although i have heard that some people use Q and you use R.. so its just all over the place really. use any letter you want i rekon thats the problme with maths, you have so many teachers teaching their own little different ways, (because they think their so good) but you go to another school or classroom with the same subject, and people will be like WDF does this mean etc. i wish everything was taught uniformly. be so much easier (but that would never happen)

 

[hscmathstutor10]

Iv'e be taught to use capital M.....although i have heard that some people use Q and you use R.. so its just all over the place really. use any letter you want i rekon thats the problme with maths, you have so many teachers teaching their own little different ways, (because they think their so good) but you go to another school or classroom with the same subject, and people will be like WDF does this mean etc. i wish everything was taught uniformly. be so much easier (but that would never happen)

its all about the method, yes you can use any letter you want

 

[MrBrightside]

its all about the method, yes you can use any letter you want

yes i know the method very clear and well, its just applying it the correct way on tricky qs that I know will get to me.

 

[hscmathstutor10]

sorry to disappoint but that is no where near what would be considered a hard financial question

 

[MrBrightside]

sorry to disappoint but that is no where near what would be considered a hard financial question

I never said it was hard, i was refering to other tricky qs.

 

[Alkanes]

jesus same shit dude. and agreed with hscmathstutor10 i think he's a better maths teacher than your teacher LOL :L

 

[Alkanes]

and btw these type of loan repayment questions aern't that hard they're average.. the only thing u think is hard becos it's shit as long thats all, otherwise it's not that bad.

 

[deterministic]

Iv'e be taught to use capital M.....although i have heard that some people use Q and you use R.. so its just all over the place really. use any letter you want i rekon thats the problme with maths, you have so many teachers teaching their own little different ways, (because they think their so good) but you go to another school or classroom with the same subject, and people will be like WDF does this mean etc. i wish everything was taught uniformly. be so much easier (but that would never happen)

This is why you STATE what each letter represents before using it. Using a different letter does not really constitute a different method.

 

[Riproot]

Iv'e be taught to use capital M.....although i have heard that some people use Q and you use R.. so its just all over the place really. use any letter you want i rekon thats the problme with maths, you have so many teachers teaching their own little different ways, (because they think their so good) but you go to another school or classroom with the same subject, and people will be like WDF does this mean etc. i wish everything was taught uniformly. be so much easier (but that would never happen)

I've*
Yeah, my teacher uses M and she's excellent, but I use R just because I think R=Repayment, I had seen it like nowhere until now.

 

[ibbi00]

HSC exams use 'P' to denote repayment. If anything, that's the 'standard'.