My Math Forum Finance problems (Annuities) help!!

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 January 30th, 2014, 03:11 PM #11 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Finance problems (Annuities) help!! Show whatever work you're able to do, it will help us guide you. (And maybe even start a new thread for the new problem.)
January 30th, 2014, 03:28 PM   #12
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Re: Finance problems (Annuities) help!!

Quote:
 Originally Posted by CRGreathouse Show whatever work you're able to do, it will help us guide you. (And maybe even start a new thread for the new problem.)

Ok well here goes:

Since we're going to withdraw 45k for 35 years, I did 45k * 35 = 1,575,000. We'll need this money for retirement.
I will use the financial calculator to calculate the present value. I would input 1,575,000 for FV, then 22*52 = 1,144 for N (because it's compounded weekly over 22 years)
Further, I would input 3.25%/52 = 0.063% for I.

Then I would compute PV, which gives me $766,256 . However, I went to see the teacher and she said this was the wrong answer... she didn't want to explain why. I'm guessing it has either something to do with the salary increase of 2% per year (that I have no idea what to do with), or the goal is not the find the PV, but the first payment? That's all I could come up with... can someone lend a hand? January 31st, 2014, 05:43 AM #13 Global Moderator Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Finance problems (Annuities) help!! So the interest per year should be (1 + 0.035/52)^52 - 1 or about 3.56%. Quote:  Originally Posted by Noritaka Since we're going to withdraw 45k for 35 years, I did 45k * 35 = 1,575,000. We'll need this money for retirement. Probably you'll need a bit less, since you'll earn interest during retirement too. For the 35th year you will need 45,000. For the 34th year you'll need 45,000 plus enough to have 45,000 for next year after a year's interest which is 43,452 for a total of 88,452. For the 33rd year you will need 45,000 plus enough to have 88,452 after a year's interest or 85,411 for a total of 130,411. Working backward like this I get a requirement for about 1,037,707.60 -- though this depends on how to interpret weekly interest and so your number might come out slightly different. Then you need to work out how much they need to make to get to this number. If their first deposit is x they have x after the first year. After the second year they have about 1.0356x (last year's total, plus interest) plus 1.02x (this year's earnings, with their 2% raise) for a total of about 2.0556x. With interest this becomes about 2.1288x for the next year, plus 1.0404x for this year's earnings, etc. After 22 years I get a total of about 45.8693x (subject to the same caveat as above on weekly interest). At this point it's easy to solve for the amount needed, just divide the million-dollar figure by 45ish to get 22,623.16.  January 31st, 2014, 01:28 PM #14 Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Re: Finance problems (Annuities) help!! Code: YEAR TRANSACTION INTEREST BALANCE 1 22,712.37 0 22,712.37 2 23,166.62 808.73 46,687.72 ... 21 33,749.38 27,324.60 828,456.89 22 34,424.37 29,499.30 892,380.56 01 -45,000.00 31,775.46 879,156.02 02 -45,000.00 31,304.56 865,460.58 ... 34 -45,000.00 3,041.29 43,452.76 35 -45,000.00 1,547.24 .00 Above shows requirements IF there is a 1 year span between last deposit and 1st$45,000 withdrawal; the wording of your problem is hard to follow...also above assumes a 2% annual increase to the deposits, plus assumes the 3.5% rate is effective for the whole 57 years period. The required account balance at end of year 22 (892,380.56) and the initial deposit (22,712.37) can both be calculated by standard financial formulas. However, you don't seem interested in formulas, only the answers, so I won't bother. I'm saying that because you keep refering to a "calculator"... Is that what you're after: what to enter and how to operate your calculator? Guess you can't be faulted for that, with a 1 hour per week teacher
 January 31st, 2014, 01:46 PM #15 Newbie   Joined: Jan 2014 Posts: 11 Thanks: 0 Re: Finance problems (Annuities) help!! Hey thanks alot for the help guys! Denis, I'm not interested only in answers, but how to get them! After all, I have a midterm next week! And yes, I rely heavily on my financial calculator to help me out! So just to make sure, sorry for the stupid question, but is the amount required at the start of the retirement 892,380.56 like Denis calculated, or 1,037,707.60 like CRG calculated? And Denis, how did you get the 892,380? I plugged in N = 35, I = 3.56%, and PMT = 45000, and computed the PV, it gave me $892,474.60. There's almost a$100 difference. What am I doing wrong?
January 31st, 2014, 01:56 PM   #16
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Re: Finance problems (Annuities) help!!

Quote:
 Originally Posted by Noritaka And Denis, how did you get the 892,380? I plugged in N = 35, I = 3.56%, and PMT = 45000, and computed the PV, it gave me $892,474.60. There's almost a$100 difference. What am I doing wrong?
(1+.035/52)^52 - 1 = .03560751575...so use 3.560751575 if you want precision!
A $100 difference doesn't take much! Will you be allowed your calculator during the exam/test? If you need the formulas, let me know; did you search for formulas, using google? Are you also "Marcipanas", the person who posted almost your identical question? January 31st, 2014, 02:22 PM #17 Newbie Joined: Jan 2014 Posts: 11 Thanks: 0 Re: Finance problems (Annuities) help!! Quote: Originally Posted by Denis Quote:  Originally Posted by Noritaka And Denis, how did you get the 892,380? I plugged in N = 35, I = 3.56%, and PMT = 45000, and computed the PV, it gave me$892,474.60. There's almost a $100 difference. What am I doing wrong? (1+.035/52)^52 - 1 = .0356075.... A$100 difference doesn't take much!

Are you also "Marcipanas", the person who posted almost your identical question?

Thanks, now it's working! I get 892 380. Now I am trying to get 22,712.37. I plug in Fv = 892 380, I = 3.56075, N = 22, but the PV is giving me 413,290.77! How do you find 22,712.37 with the formula or calculator?

And no, that is not me! Odd that his question resembles mine though ...

January 31st, 2014, 07:45 PM   #18
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Re: Finance problems (Annuities) help!!

Quote:
 Originally Posted by Noritaka Now I am trying to get 22,712.37. I plug in Fv = 892 380, I = 3.56075, N = 22, but the PV is giving me 413,290.77! How do you find 22,712.37 with the formula or calculator?
You need the formula...financial calculators usually don't handle this (you can't input the 2%, right?).
Here's how you'd do the full problem without a financial calculator:

GIVENS: r = .035, j = .02, p = 45000, n = 22, m = 35

Step 1; convert rate:
i = (1 + r/52)^52 - 1 : .035607515937....

Step 2; get required value v at end of n years:
v = p[1 - 1/(1 + i)^m] / i : 892380.56267717....

Step 3; get 1st deposit d (which increases by j annually) which will accumulate to v :
d = v(i - j) / [(1 + i)^n - (1 + j)^n] : 22712.3699508....

Again, note that I'm assuming the 1st withdrawal is 1 year after the last deposit.
Hope that helps...

 February 1st, 2014, 12:32 PM #19 Newbie   Joined: Jan 2014 Posts: 11 Thanks: 0 Re: Finance problems (Annuities) help!! Ok thanks, I think I understand the concept now!
 May 19th, 2014, 04:17 AM #20 Newbie   Joined: May 2014 From: pakistan Posts: 3 Thanks: 0 annuity i have a qs regarding annuity? a bank offers a car loan for car above Rs.3000000 tax free.a man likes a car worth 110% more than the lower limit.he keep some of the money in the bank and lease the car from the bank using the left over money.he keeps 70% in the bank,gives the car initial payment with the rest and takes the out.the bank gives an interest of 8% on the deposited money.to lease the car he has two options,he can get a simple interest of 6% per month over 2 years or a compound interest of 3% per month over 4 years.the car he bought was tax by the government at 15%, had to pay to the bank. if he originally had 7000000 to begin with,which scheme is better assuming that he has other sources of income and the bank decides to distribute the total loan and interest equally each month.give answer in terms of annuity? if the inflation rate runs at 7% per annum,considering the future rice of car and the laon scheme man opted for,now was getting a car on lease a wise option?

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### SIMPLE INTEREST ON 45,000FOR 5 YEARS AT 6/ PER ANNUM.

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