Problem with Annuities - What to do when you dont get the right answer.... (1 Viewer)

[JoyDivision]

Hello All.

A friend and I are absolutley stumped on this question because our answers arent matching up to Mr. Textbook. So heres the steps ive been taking with the question - any help would be totally and utterly appreciated.


'A Single Income family has saved $24,000 towards the cost of a home unit which they are able to purchse for $110,000'

A) How much will they have to borrow (at least?) = $86,000

B) The interest rate on the loan is 7.30% p.a. and they are advised to take the loan over 25 years

i) How much will each monthy installement be? (The problem question)

The steps I am taking -

1) N=M [ (1+r) n - 1]
------------------
r (1 + r ) n


2) N = $86,000
r = 0.0061 (7.30 divided by 12)
n = 300 (12 times 25)

3) 86,000 = M [ (1+ 0.0061) 300 - 1 ]
----------------------------
0.0061 (1 + 0.0061) 300

4) M = 86,000 x 0.0061 (1.0061) 300
--------------------------------------
(1.0061) 300 - 1


ANSWER = $523.60


The textbook says the answer is $624.39

Could you please help in any way, shape or form? This question is driving me crazy.

 

[glitterfairy]

sure thing!

I think your main problem was the rate - remember, it's a percentage, so 7.3% is really 0.073 over 12.

Best wishes!

 

[PC]

I think your problem might be that you rounded off too much. You've really only got 2 sig figs to work with with the rate, but the amounts are about five sig figs. Anyway ... how does this go.

Because this is a loan, the amount borrowed becomes the present value.
So N = 86000
The interest rate is 7.30% p.a., or 0.60833...% per month, or 0.00608333... as a decimal.
The length of time is 25 x 12 = 300 months
And put this into your formula.
I got $624.3869181 = $624.39

If you are using a GC then:
n = 300
I = 7.30
PV = -86000
PMT = 0 (this is what we're working out)
FV = 0
P/Y = 12
C/Y = 12
Press [F4] for PMT, and get ... $624.3869204 = $624.39

Hope this helps!

All the best for tomorrow!

 

[JoyDivision]

Thanks a lot guys for your quick and helpful responses.

We did end up working it out after I'd come on here and we like sat down and had a heart to heart with our caculators. The problem was yeah, I was rounding off too much and that I was also demanding too much of the calculator, like plugging it all in at once rather than just getting answers as I went.


But yeah, thanks again and good luck to you too if either of you are doing the HSC.