Question

FINITE MATH: How do I solve this problem? A person invests $2000 annually in an IRA. At the end of 6 years, the amount in the fund is $14000. What annual nominal compounding rate has this annuity earned? (use graphical approximation techniques or an equation solver to approximate the desired interest rate.)

FV=PMT (1+i)^n -1 /1
14000=2000 (1+i)^n -1 /1

I don't know where to go next! Please help if you can.

Answer 1

So, if the person invest $2000 every year, at the end of 6 years they should have (with no earnings) $12000

2000 x 6 = 12000

Although, the person now has $14000, which is $2000 earnings.

How much % is $2000 compared to $12000?

12000 x Y = 2000 (=) Y = 2000/12000 (=) Y = 0.16(6) (=) Y = (aprox) 17%

I think this is what your problem is asking, but can't be sure.

Answer 2

I do not know what annual nominal compounding rate means, but i'm guessing it's the interest...

Answer 3

Thank you FS appreciate your response. It is interest. we are supposed to set up the problem using the FV method.

Answer 4

Hi Jannellsm98,
That type of investment is an annuity and here is a calculator for that
http://1728.org/annuity.htm
Here are three annuity formulas (each is solved for one of three variables - (principal, beginning amount and ending amount).

Unfortunately, the annuity formula cannot be solved for rate but let's see what we can do.
The calculator gives an answer of 4.4213%
Let's try the formula solved fir TOTAL
Total = ([amount*(1+rate)^(n+1) -1] / rate) - Amount
Total = [2,000 * (1+.044213)^(6+1) -1] / .044213 ] - 2,000
So, the rate appears to be correct.

Answer 5

Thank you wolf appreciate your response. I am going to try and work the problem you provided to see if I can do it. THank you again.

Answer 6

I do not knot why you were given this problem in which you must solve for rate. (The TOUGHEST of the 4 annuity variables you have to solve).

Answer 7

It HAS to be solved using trial and error. An exact, precise formula cannot be calculated to solve for rate.

Answer 8

In case you are wondering how does MY calculator solve for rate? Yes, it uses a trial and error routine to save the user from doing all that work.

Answer 9

If you are trying to work through the problem, I'd suggest you use an electronic spreadsheet (Excel, OpenOffice, etc)
i'm willing to help you with this. :-)

Answer 10

Thank you so much. I have been so stressed and working on this for over 24 hours. I just went to the website you referenced. It was a great tool. I am going to have to show work when submitting. this was tough and this is the 2nd time I have taken this class due to poor grade previously.

Answer 11

Is this just an introductory course? By that I mean you are not taking this course to earn a PhD in financial formulas right?
If they are expecting you to solve for the rate of an annuity, they have NO IDEA how to present INTRODUCTORY mathematical materials. Also, if this is the second time you are taking this course, how much of this is their fault as opposed to your fault?

Answer 12

No I am actually working on my Bachelor's in Psych. Go figure. LOL. I got a 1.8 in the class previously. I have bad math anxiety bcuz of it.

Answer 13

Since you must show your work, it cannot be shown as a nice neat tight mathematical procedure. No it is a trial and error process. Again you must learn how to use Excel or OpenOffice). I highly recommend OpenOffice because
1) it is NOT Microsoft and
2) it is free and easily available online.

So, now that Open Office is downloaded and ready to go, let's set up a formula.
=(2000*(((1+B12)^7)-1)/B12)-2000
Notice it starts with an equal sign?
The 2,000 is the amount invested annually, the '7' is the number of years plus one,
B12 is a rate that is input in cell B12
So to start, we will first choose .08 for the rate which produces a total of
15,845.61 which is higher than 14,000 so the rate must be lower that that.
Let's choose 4 % which gives us a total of
13,796.59. So 4% is too low, so next we'll choose 5% which calculates to
14,284.02 which is too high. Continuing to take smaller values for the rate

rate? total? high or low?
4.5 14,038.30 High
4.25 13,916.95 Low
4.375 13,977.50 Low

Well, you can continue proceeding like that or if you know how to use spreadsheets, you could make 10 rows of rates that go from .0440 to 0.0450000
and get totals of
13,989.64
13,994.50
13,999.36
14,004.22
14,009.09
14,013.95
14,018.82
14,023.69
14,028.56
14,033.43
Then see results when you choose rates one tenth of these.

Answer 14

Thank you again. You are a rockstar. I could only dream of being able to conquer math like you did that problem.

Answer 15

Anyway, let me know specifically what you have to do to "show your work". I'll be happy to help you out. I'm glad you like the links I posted - that's my website :-)

Answer 16

Attached is an electronic spreadsheet which solves for the rate by using 7 trial and error steps.