Question 241276: The present value of an account earning 8 percent interest compounded monthly is $2400. An investor needs the account to be worth $4800 two years from now. How much must he contribute monthly?
i have worked on it and every time i get a wrong answer this is how i set up my problem: FV=PV(1+i)^M
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you're using the wrong formula.
here's a list of the formulas you should use for the type of problems you will encounter mostly.
LIST OF FINANCIAL FORMULAS
The particular formula you are interested in is:
PAYMENT FOR A FUTURE VALUE
PMT = Payment per time period
FV = Future Value
i = Interest Rate per Time Period
n = Number of Time Periods
You do, however, have to make an adjustment.
You start off with $2400 and you want to end up with $4800.
The formula assumes the starting value is $0.
You need to subtract $2400 from the $4800 so that your starting value is $0 and your ending value is $2400.
You can then substitute in the formula as follows:
where:
FV = future value = $2400
i = .08/12 = .0066666667
n = 2*12 = 24
Now you can use the formula as follows:
This becomes
which becomes:
which becomes:
The future value of your payments will be $2400.
Add this to the $2400 that you started with and you will have $4800.
Because you were compounding monthly, your annual interest of 8% needed to be divided by 12 and converted to a straight rate before plugging into the formula.
8% / 12% = .666666667% / 100% = .0066666667.
Your number of years needed to be multiplied by 12 in order to get number of months because your payments were on a monthly basic and your compounding of interest was on a monthly basis.
That's why we multiplied 2 years by 12 to get 24 months.
Once everything was in sync, you could use the formula.
The formula you were using was not a payment formula.
It was a future value of a present amount formula.
You could not solve for payments using that formula.
you can confirm your answer is correct by plugging the value of the payment back into the original formula.
I used a financial calculator which is the easiest way if you know how to use it.
You can also used financial formulas in EXCEL if you know how to use them and you have a copy of EXCEL on your computer.
There are also financial calculators on the web that you can use to check your work if you know how to use them.
If you are interested in one, let me know and I'll scour the web for you.
They can help, but you do have to know how to use them based on the problems you have to solve.
Example is your problem. If you didn't know that you had to subtract the present value to use the formula, you never would find the correct answer.
I MADE A MISTAKE.
I assumed the $2400 was NOT earning any money.
That changes the problem.
Big time.
Since the $2400 is invested also, then the problem changes as follows:
You first calculate the future value of the $2400 already invested in the account.
That comes out to be (using your original formula)
FV(PA) = $2400 * (1.006666667)^24 = $2814.931036
That's what $2400 earns in 2 years compounded monthly.
THAT's the amount you have to subtract from your $4800.
The result of that subtraction is what you need to make by plugging it into the payment for a future value formula.
$4800 - 2814.931036 = 1985.068964.
The payment formula becomes:
PMT(FV) now comes out to be:
PMT(FV) = $76.54549949
You have $2400 in the account that earns you $2814.931036 by the end of 2 years.
You have payments of $76.54549949 per month that earn you $1985.068964 by the end of 2 years.
You add up $2814... and $1985... and you have $4800 at the end of 2 years.
To show you how this actually works in the account, I'm going to cut the number of months down to 5 because 24 months is too many months to show in such detail.
The future worth of $2400 at .0066666667 interest per month for 5 months is equal to $2481.073802
The future worth of $76.54549949 payments for 5 months is equal to $387.8646645
Total future worth is $387.8646645 + $2481.073802 = $2868.938467
This is the money you will have in the account after 5 months.
Here's how it works:
all numbers truncated on display but full numbers used for calculations.
At end of month 1 you will have $2400 * 1.0067 + $76 = $2492.5
At end of month 2 you will have $2492.5 * 1.0067 + $76 = $2585.7
At end of month 3 you will have $2585.7 * 1.0067 + 76 = $2679.4
At end of month 4 you will have $2679.4 * 1.0067 + 76 = $2773.9
At end of month 5 you will have $2773.9 * 1.0067 + 76 = $2868.938466
The number calculated in detail after 5 months is the same number we calculated using the future value of present value formula and the payment for a future value formujla.
The same process applies to your problem except you carry it out 24 months instead of 5.
Sorry for the mistake but it was instructive so I left it in. The mistake I made would be a common mistake if you didn't know better. I should have.
You needed to break your problem into two parts.
The first part was the initial investment where you used the formula you started with.
You used this to calculate what the initial investment would be worth at the end of the 2 years.
You then subtracted that amount from $4800 so you could calculate how much payments you needed to make each month to come up with the difference.
At the end, the sum of the future value of your initial investment plus the sum of the future value of the payments needed to be equal to $4800.
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