Help in Future Value Problem

[MathMathMathMathMathMath]

Hello everyone, im a HS Senior taking Algebra, and our teacher left us with a project dealing with Future Values and Present Values, we were told that this would be something that we will encounter a lot in our adult lives so he is giving us a little taste of it. I am not really sure on how I am supposed to start to recalculate this. What I have come up with is multiplying the numbers numbers by 4000/9859, and from years 45 to 65 multiplied by 4000/9858. I am stuck and I am not sure how to start it. Any clues on how to start would be very helpful. This is the first time that I have dealt with this type of problem. Thanks.
Future Value Problem:
How much could you save for retirement at age 65, (I am supposed to change this from 65 to 45)
if you started saving at age 22? (I am supposed to change this from 22 to 25)
After these changes I need to recalculate, so the numbers below will change. How do I do this? Help me out please I have no Idea how to start so helping me recalculate would be great.

Age at beginning of IRA saving: 22
Retirement Age: 65
Beginning annual salary: $40,000
Annual raise: 4.0%
Annual rate of return: 8.0%
Annual withholding: 10.0%
Company matching: 50.0%

Current Value Current Value Future Value
Age Employee Cont. W/Employer Match Annual Investment
22 ------$4,000 --------$6,000 ---------- $164,200
23 ------$4,160 --------$6,240 ---------- $158,118
24 ------$4,326 --------$6,490 ---------- $152,262
25 ------$4,499 --------$6,749 ---------- $146,623
26 ------$4,679 --------$7,019 --------$141,192
27 ------$4,867 --------$7,300 --------$135,963
28 ------$5,061 --------$7,592 --------$130,927
29 ------$5,264 --------$7,896 --------$126,078
30 ------$5,474 --------$8,211 --------$121,409
31 -------$5,693 --------$8,540 --------$116,912
32 -------$5,921 --------$8,881 --------$112,582
33 -------$6,158 --------$9,237 --------$108,412
34 -------$6,404 --------$9,606 --------$104,397
35 -------$6,660 --------$9,990 --------$100,530
36 -------$6,927 --------$10,390 --------$96,807
37 -------$7,204 --------$10,806 --------$93,222
38 -------$7,492 --------$11,238 --------$89,769
39 -------$7,792 --------$11,687 --------$86,444
40 -------$8,103 --------$12,155 -------$83,243
41 -------$8,427 --------$12,641 --------$80,159
42 -------$8,764 --------$13,147 --------$77,191
43 -------$9,115 --------$13,673 --------$74,332
44 --------$9,480 --------$14,220 --------$71,579
45 --------$9,859 --------$14,788 --------$68,928
46 --------$10,253 --------$15,380 --------$66,375
47 --------$10,663 --------$15,995 ---------$63,916
48 --------$11,090 ---------$16,635 ---------$61,549
49 -------$11,533 --------$17,300 --------$59,270
50 -------$11,995 --------$17,992 --------$57,074
51 -------$12,475 --------$18,712 --------$54,960
52 --------$12,974 --------$19,460 --------$52,925
53 --------$13,493 ---------$20,239 --------$50,965
54 --------$14,032 ---------$21,048 --------$49,077
55 -------$14,594 --------$21,890 --------$47,259
56 -------$15,177 --------$22,766 --------$45,509
57 -------$15,784 -----------$23,677 --------$43,824
58 -------$16,416 --------$24,624 --------$42,201
59 -------$17,072 --------$25,609 --------$40,638
60 -------$17,755 --------$26,633 ---------$39,132
61 -------$18,465 --------$27,698 ---------$37,683
62 -------$19,204 --------$28,806 --------$36,287
63 -------$19,972 --------$29,958 --------$34,943
64 -------$20,771 --------$31,157 --------$33,649
65 -------$21,602 --------$32,403 --------$32,403


=3,590,918

** FV(IRA)=P + P*(1+r) + P*(1+r)^2 +…+ P*(1+r)^n

(this was on a spread sheet i just copy pasted it on here and added the lines between the numbers to seperate them)

 

[Deleted member 4993]

Future Value Problem:
How much could you save for retirement at age 65, (I am supposed to change this from 65 to 45)
if you started saving at age 22? (I am supposed to change this from 22 to 25)
After these changes I need to recalculate, so the numbers below will change. How do I do this? Help me out please I have no Idea how to start so helping me recalculate would be great.

Age at beginning of IRA saving: 22
Retirement Age: 65
Beginning annual salary: $40,000
Annual raise: 4.0%
Annual rate of return: 8.0%
Annual withholding: 10.0%
Company matching: 50.0%

Current Value Current Value Future Value
Age Employee Cont. W/Employer Match Annual Investment
22 ------$4,000 --------$6,000 ---------- $164,200
23 ------$4,160 --------$6,240 ---------- $158,118
24 ------$4,326 --------$6,490 ---------- $152,262
25 ------$4,499 --------$6,749 ---------- $146,623
26 ------$4,679 --------$7,019 --------$141,192
27 ------$4,867 --------$7,300 --------$135,963
28 ------$5,061 --------$7,592 --------$130,927
29 ------$5,264 --------$7,896 --------$126,078
30 ------$5,474 --------$8,211 --------$121,409
31 -------$5,693 --------$8,540 --------$116,912
32 -------$5,921 --------$8,881 --------$112,582
33 -------$6,158 --------$9,237 --------$108,412
34 -------$6,404 --------$9,606 --------$104,397
35 -------$6,660 --------$9,990 --------$100,530
36 -------$6,927 --------$10,390 --------$96,807
37 -------$7,204 --------$10,806 --------$93,222
38 -------$7,492 --------$11,238 --------$89,769
39 -------$7,792 --------$11,687 --------$86,444
40 -------$8,103 --------$12,155 -------$83,243
41 -------$8,427 --------$12,641 --------$80,159
42 -------$8,764 --------$13,147 --------$77,191
43 -------$9,115 --------$13,673 --------$74,332
44 --------$9,480 --------$14,220 --------$71,579
45 --------$9,859 --------$14,788 --------$68,928
46 --------$10,253 --------$15,380 --------$66,375
47 --------$10,663 --------$15,995 ---------$63,916
48 --------$11,090 ---------$16,635 ---------$61,549
49 -------$11,533 --------$17,300 --------$59,270
50 -------$11,995 --------$17,992 --------$57,074
51 -------$12,475 --------$18,712 --------$54,960
52 --------$12,974 --------$19,460 --------$52,925
53 --------$13,493 ---------$20,239 --------$50,965
54 --------$14,032 ---------$21,048 --------$49,077
55 -------$14,594 --------$21,890 --------$47,259
56 -------$15,177 --------$22,766 --------$45,509
57 -------$15,784 -----------$23,677 --------$43,824
58 -------$16,416 --------$24,624 --------$42,201
59 -------$17,072 --------$25,609 --------$40,638
60 -------$17,755 --------$26,633 ---------$39,132
61 -------$18,465 --------$27,698 ---------$37,683
62 -------$19,204 --------$28,806 --------$36,287
63 -------$19,972 --------$29,958 --------$34,943
64 -------$20,771 --------$31,157 --------$33,649
65 -------$21,602 --------$32,403 --------$32,403


=3,590,918

** FV(IRA)=P + P*(1+r) + P*(1+r)^2 +…+ P*(1+r)^n

(this was on a spread sheet i just copy pasted it on here and added the lines between the numbers to seperate them)

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Since you are stuck in the beginning, start by defining the variables in the equation that you have posted (FV, P, r and n) :

FV(IRA)=P + P*(1+r) + P*(1+r)^2 +…+ P*(1+r)^n


Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[MathMathMathMathMathMath]

Reply

Ok thank you. FV is the Future Value. P is initial amount which would be $40,000. R is the rate of interest per year which would be 10.00% and N is the period in years. Since I would have to change the number of years that means that there would only be 30 rows which would be 30 years.

 

[Deleted member 4993]

Did you check the cells for pertinent formula?

 

[JeffM]

I agree, of course, with Subhotosh Khan that you should define what symbols mean what, but the way the process has been symbolized by your teacher (or by you) seems to be highly misleading. Furthermore, P is certainly NOT 40,000.

It probably should be stated as \(\displaystyle F = P_n + P_{(n-1)}(1 + r) + P_{(n-2)}(1 + r)^2 + ... P_1(1 + r)^{(n - 1)} = \displaystyle \sum_{i=1}^n\left\{P_i(1 + r)^{(n - i)}\right\}.\)

The above matches what the spreadsheet seems to be doing, and what the spreadsheet seems to be doing makes sense. (I can't be sure of course what the spreadsheet is doing because you have not included the formulas from it.)

See if you can define F, P_i, r, and n now that you have a symbolization that seems to match the spreadsheet. Clue: you had F, r, and n right the first time.