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If I want to buy a new car 8 years from now that will cost $30000.In order to meet this goal, how much money must I save annually, if the funds earn an interest rate of 12%?
I did next:
FV=30000
I/Y=12
N=8
COMP and I have PV=19582.05
am I right or should I go with
FV=30000
I/Y=12
N=8
COMP and I have PMT=584.10
please, let me know where I'm wrong!!
One needs to go in stages here:-
1) Test with $2,000 per year. One gets these answers.
1 2,000.00 2,240.00
2 4,240.00 4,748.80
3 6,748.80 7,558.66
4 9,558.66 10,705.69
5 12,705.69 14,230.38
6 16,230.38 18,178.02
7 20,178.02 22,599.39
8 24,599.39 27,551.31
As you can see $2,000 is insufficient.
So now we need to get the right amount
Per year from the above.
See next the sufficient amount:-
BY PROPORTION
2,000.00 27,551.31
2,177.75 30,000.00
The new annual amount needed is $2,177.75.
The proof is as follows:-
1 2,177.75 2,439.08
2 4,616.83 5,170.85
3 7,348.60 8,230.43
4 10,408.18 11,657.16
5 13,834.91 15,495.10
6 17,672.85 19,793.60
7 21,971.35 24,607.91
8 26,785.66 29,999.94
You need to go through all the calculations
And understand them.
An EXCEL spreadsheet will help you get there.
However you must understand the mathematics.
Good luck
I don't get the point in the "stages" or why you need to test $2000. There isn't any point to that, unless you just want to see it. You also do not need to use Excel. It looks like you're using a financial calculator to do this. If that is what is required in class or the way you choose to do it, that is fine. (And Rolcam, there is absolutely no explanation in your answer of how you came up with any of that stuff.)
What you're messed up on to begin with is in deciding if this is an annuity or not. If you're going to "make payments annually" it's an annuity. An annuity involves some type of payment, either being put into something or taken out of something. When you have payments like that, NEVER use FV and PV together. They won't exist together like you tried to do first. (It only works for lump sums, e.g. you stick money into something and just let it sit and earn interest, but don't add more payments to it.)
This is a sinking fund - making payments to save up for something you need in the future. That's always an annuity.
So your second attempt is the basic idea. Except that I don't know how you got your answer. If you're using a calculator, it means you're entering it into the calculator incorrectly somehow. As a matter of fact, even if this were a lump sum instead of an annuity, you first answer isn't correct. So I'm not sure what you're doing wrong in the calculator.
You've got the N=8, I/YR=12, FV=30,000. That's all OK. Some ideas:
You didn't include P/YR (or whatever yours calls it). That is, you have 1 payment per year. It needs to know how often it's compounding.
With my calculator, whatever I stick into these keys will stay. If I do a new problem, anything I don't replace stays there. For instance, if I did one where I used PV and this problem doesn't use it, the PV from the prior problem stays there and gets calculated into the thing screwing it up. I have to "clear" anything I don't want (and the answer I want in case I used it) by entering zero.
For instance, I entered N=8, I/YR=12, PV=0 (to clear), PMT=0 (to clear, even though that's the answer I want), FV=30,000, and P/YR=1. Then I hit the PMT key to get my answer. I don't know if your calculator has this issue.
I assume COMP is compute, but you aren't telling it what to compute that I can see. Something is just seems missing somewhere.
As for the 2177.75 Rolcam came up with, that's based on the assumption of an annuity due. That's when payments are made at the beginning of the period. Unless the problem says otherwise, it's generally assumed to be at the end of the period. Does the problem say anything about this? (Don't leave things out of problems when you present them to us.) If not, I'm assuming at the end of each year.
It is something wrong with my calculator, so I'm trying to have it done by myself.
I thought that the $30,000 represents the Future Value of the amount I need to save annually.
The annual savings would represent an annuity
and the FV of annuity is calculated as follows:
FVan=C*((1+R)^-1)/R (from my book)
and C=2439.02
In my calculations the amount payable
Every year is $2,177.75.
This is payable at the beginning of the year.
This amount has to be paid in every beginning of the year for 8 years.
... which would be correct, if you're making 8 deposits to the interest-bearing savings account, with the first deposit being made one year from today, and the 8th just becomes available to you the day you buy the car.Quote:
Originally Posted by sasham
As ROLCAM explains, 2,177.75 is the annual payment needed if you make your first deposit today, and the 8th occurs one year prior to purchasing the car.
Your first order of business is exactly what Morgaine300 suggested: Check the problem carefully to determine the timing of the annual payments contemplated in the problem.
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