
Economics Economics Forum  Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance 
 LinkBack  Thread Tools  Display Modes 
January 21st, 2012, 05:20 AM  #11  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Very difficult question (need help) Quote:
I think you used .10/12 as rate: slightly too high: rate compounds semiannually, not monthly. .10/12 = .008333.... ; should be .008164... It is USUAL to make the interest rate factor match the frequency of payments.  
January 21st, 2012, 10:49 AM  #12  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Very difficult question (need help) Quote:
Code: j = 10% i = 12% Year Deposit Interest Balance 0 .00 .00 .00 1 1000.00 .00 1000.00 2 1100.00 120.00 2220.00 3 1210.00 266.40 3696.40 F = Future value (?) D = initial deposit (1000) j = deposit increase (.10) i = interest rate (.12) n = number of years (3) F = D*[(1 + i)^n  (1 + j)^n] / (i  j) F = 1000(1.12^3  1.10^3) / (.12  .10) = 3696.40 Basically all that simple...google will give ya lotsa sites, like: http://www.financeformulas.net/Growing ... Value.html  
January 21st, 2012, 07:33 PM  #13  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Very difficult question (need help) Quote:
 
January 21st, 2012, 07:49 PM  #14  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Very difficult question (need help) Quote:
This is a present value relative to the withdrawals, payments growing at 5% annually, but earning (we assume) 10% semiannually. That equation is growing to a future value, not shrinking from a present value.  
January 22nd, 2012, 06:00 AM  #15  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Very difficult question (need help) Quote:
This was the rate per the problem: "in an account that earns an average of 10% compounded semiannually". 10% cpd semiannually means 10.25% annually ; 1.05^2  1 = .1025 So the problem statement could as well be: ....10.25% compounded annually (same thing). It is standard practice to convert the effective ANNUAL rate such that it matches the payments frequency; on this case, to 12 periods annually; so: (1 + i)^12 = 1.1025 ; i = .0081648... So the "semiannual equivalent deposit" is ~1852.14, not ~1853.24. Another example:If given rate is 12% annual cpd. quarterly and payment frequency is 6 (every 2 months), then equivalent rate becomes: (1 + i)^6 = (1 + .12/4)^4 ; i = .019901...slightly lower than 2%, as expected.  
January 22nd, 2012, 06:19 AM  #16  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Very difficult question (need help) Quote:
I used it that way because (being lazy) it was easier to "do the typing"! Take the ending balance of 3696.40 and get its Present Value: 3696.40 / 1.12^3 = ~2631.02. So this means that if a payment of $1000 increasing by 10% yearly is made for 3 years, then the amount that can be "borrowed" is $2631.02 Code: j = 10% i = 12% Year Payment Interest Balance 0 .00 .00 2631.02 1 1000.00 315.72 1946.74 2 1100.00 233.61 1080.35 3 1210.00 129.65 .00 of $132,691.91 yearly increasing by 5% yearly would basically be obtained the same way. So you don't scold me again(!), here's the direct formula: P = Payment (?) A = Amount borrowed (2631.02) n = number of periods (3) i = interest rate (.12) j = payment increase (.10) P = A(i  j) / [1  (1 + j)^n / (1 + i)^n] P = 2631.02(.12  .10) / (1  1.10^3 / 1.12^3) = 1000  
January 22nd, 2012, 09:31 AM  #17 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Very difficult question (need help)
More on "the formula"! Code: Payments accumulation Loan, no payments 0 .00 2631.02 1 1000.00 .00 1000.00 315.72 2946.74 2 1100.00 120.00 2220.00 353.61 3300.35 3 1210.00 266.40 3696.40 396.05 3696.40 the loan in a separate account; both accounts end up the same, of course. The "payments account" is looked at this way: 1000(1.12)^2 = 1254.40 1100(1.12)^1 = 1232.00 1210(1.12)^0 = 1210.00 ==================== total.......... = 3696.40 So the requirement is made up of a SUM; this is shown as such in Mark's formula. The formula I've shown produces same results, in a direct way. 
January 22nd, 2012, 10:28 AM  #18 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Very difficult question (need help) Code: # DATE DEP/WD INTEREST BALANCE 1 Jan.1/1 300.00 .00 300.00 2 Feb.1/1 300.00 2.45 602.45 3 Mar.1/1 300.00 4.92 907.37 .... 419 Nov.1/35 300.00 8,680.68 1,072,157.77 420 Dec.1/35 300.00 8,754.00 1,081,211.77 1 Jan.1/36 133,978.13 8,827.93 956,061.57 2 Jan.1/37 140,677.04 97,996.31 913,380.84 .... 9 Jan.1/44 197,946.72 36,694.91 196,747.71 10 Jan.1/45 207,844.05 20,166.63 9,070.29 KB Jan.1/46 929.71 10,000.00 : KB = Kicks Bucket! there is a 1 year period between last withdrawal and $10,000 donation, the 1st withdrawal will be $133,978.13. Quite close to Mark's $133,930.49, where $10,000 donation is not 1 year later. 
January 23rd, 2012, 02:42 AM  #19  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Very difficult question (need help) Quote:
Oh, actually, you know what. We're both right. .8333% per month is still correct, as long as you treat it like simple interest within the six month period, which is actually what I learned and should have done. (i.e. 300*.8333*6 + 300*.8333*5, etc) I just looked back at my work and realized I compounded the .8333% per month! I didn't mean to do that. (Probably sounds like the hard way, but most of my classes were using charts, not equations.)  

Tags 
difficult, question 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
DIfficult Question, try it  Iamthatdude  Math Events  1  August 28th, 2013 12:13 PM 
difficult question for matrix  frankpupu  Linear Algebra  0  February 21st, 2012 04:44 PM 
difficult question  ahmedar  Calculus  3  December 9th, 2011 12:44 PM 
Difficult question!  DragonScion  Advanced Statistics  0  October 29th, 2011 02:54 PM 
Difficult question  grahamlee  Complex Analysis  0  July 27th, 2009 09:56 PM 