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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: kddee on November 20, 2011, 04:58:06 pm

Title: NEED HELP WITH A QUESTION!
Post by: kddee on November 20, 2011, 04:58:06 pm

Kellie buys an MP3 player priced at $249 under a hire purchase scheme. She is asked to pay a deposit of $50  and to pay the balance in regular weekly instalments over the next 3 months with an effective interest rate of 22.3%. What are the weekly repayments?

Title: Re: NEED HELP WITH A QUESTION!
Post by: Deank on December 13, 2011, 06:18:07 pm

249 - 50 = 199, Interest = (Prt)/100 = (199*(22.3/12)*3)/100) = 11.094
Total = 199 + Interest(11.094) = 210.094
Weekly repayments = Total (210.094)/ Weeks(12), Assuming 4 weeks per month.
= 17.508

Not sure if correct, if anyone wants to verify or if the OP wants to post the answer.

Title: Re: NEED HELP WITH A QUESTION!
Post by: abd0l on December 25, 2011, 10:08:37 pm

249-50=199
$ Interest over 3 months: 199*(22.3/100)= 44.377
$ Total: 199+44.377= 243.377
$ Daily: 243.377/90= 2.70
$ Weekly: 2.70*7= 18.9
Not Sure :)

Title: Re: NEED HELP WITH A QUESTION!
Post by: linle on January 24, 2012, 11:05:16 pm

Cash price = 249
Deposit = 50
Balance = 249-50 = 199

P=199, r=22.3% per yr, T=3/12 yr
I=(PrT)/100=11.094

Repayment=199+11.09=210.094
Weekly payments=(210.094)/12=17.50
(the 12 is because 3 months times 4 weeks)

It seems 17.50 is the answer

Title: Re: NEED HELP WITH A QUESTION!
Post by: kddee on January 25, 2012, 07:27:03 pm

The answer is $15.77 :\

Title: Re: NEED HELP WITH A QUESTION!
Post by: linle on January 25, 2012, 11:59:47 pm

I disagree. Think about it.

3 months=12 weeks
$15.77x12=$189.24

$189.24 is under the principal value of $199.
How could you have paid it all up including interest on top?

$17.50x12=$210 and this sounds more reasonable.

Remember to always check if your answer is sensible.
Textbooks do make mistakes!

Title: Re: NEED HELP WITH A QUESTION!
Post by: kddee on January 26, 2012, 04:10:51 pm

It's a multiple choice question with answers being only:
a) $16.58
b)$19.62
c) $21.25
d) $15.77
e) $17.08

So is $17.08 the answer since it's the closest?

Title: Re: NEED HELP WITH A QUESTION!
Post by: 123456k on January 26, 2012, 04:28:49 pm

isn't effective interest different to normal interest? if i had a further maths book i could do this question. forgot all the formulas lol.

Title: Re: NEED HELP WITH A QUESTION!
Post by: 123456k on January 26, 2012, 04:33:02 pm

theres a formula for effective interest rate. what is it again?

Title: Re: NEED HELP WITH A QUESTION!
Post by: Stick on January 26, 2012, 05:07:01 pm

Effective interest rate = Flat interest rate*2n/n+1 (I think)

Title: Re: NEED HELP WITH A QUESTION!
Post by: linle on January 26, 2012, 11:58:45 pm

SOLVED!

I forgot about the effective rate of interest formula. Anyway here goes.

Effective interest rate = [(2n) / (n+1)] x flat rate (where 'n' is the number of payments)

n (number of weekly payments) = (3/12) years x 52 = 13

sub in formula to find flat rate
22.3 = [2(13) / (13+1)] x flat rate
flat rate = 12.0077 ~ 12.00

Cash price = 249
Deposit = 50
Loan = P =  199
r= flat rate = 12
T= (3/12) years

Sub in values to Simple interest formula
I = (PrT) / 100
I = 5.97

Total repayment = I + P = 204.974

Repayment = Total repayment / Number of payments
=204.974 / 13 = 15.77

*note number of payments already calculated before

Yay!