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November 1st, 2011, 07:02 PM  #1 
Newbie Joined: Nov 2011 Posts: 1 Thanks: 0  Annuities due vehicle leasing
Hi all I am doing a collage business course and part of that is financial math. I am working on a lyryx lab question related to Annuities due vehicle leasing. I am not looking for the answers just how to set up the formulas to find the answer. Now I know: purchase price down payment=pv of lease payment+ present value of the residual value. also i know: PV(due)=PMT[1(1+i)^n/i](1+i) but i do not know how to play around with the numbers to get what i need. The following is a copy and past of the question Jason is looking at leasing 4 different cars. Please fill in the missing information so Jason can make an informed decision about his purchase. For full marks your answers should be correct to the nearest cent or month. Note: MSRP = Manufacturer's Suggested Retail Price Interest Rate = Annual rate with monthly compounding MSRP DOWN PAYMENT MONTHLY PAYMENT INTEREST RATE TERM RESIDUAL VAL 27600 6000 560.22 4.75 (FIND) 9617 32500 6000 251.69 6 (FIND) 19984 54800 5000 806.33 9 36 (FIND) 30200 7000 (FIND) 5 24 14145 Also unrelated what would i do if i was asked to find MSRP or Down Payment or the interest rate 
November 2nd, 2011, 08:38 AM  #2  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Annuities due vehicle leasing Quote:
Code: MSRP DOWNPAYMENT MONTHLYPAYMENT INTERESTRATE TERM RESIDUALVAL 27600 6000 560.22 4.75 (FIND) 9617 32500 6000 251.69 6 (FIND) 19984 54800 5000 806.33 9 36 (FIND) 30200 7000 (FIND) 5 24 14145 P = Payment A = Amount borrowed n = number of periods (term) i = periodic interest rate In your 4th example (if a simple loan): P = 23200(.05 / 12) / [1  1 / (1 + .05/12)^24] = 1017.82 I think you are familiar with that, right? This leaves a zero balance owing, of course, thus no "residual value" as such. To be left with $14,145 owing (or as residual value), payment would need to be $456.19 Formula is: P = [Ai(1 + i)^n  Fi] / [(1 + i)^n  1] = 456.19 F = residual value of 14145. Finding other stuff (like n) means rearranging this formula in terms of what you're trying to find. Simplifying above to demonstrate: x = (au^n  b) / (u^n  1) ; n = ? xu^n  x = au^n  b xu^n  au^n = x  b u^n(x  a) = x  b u^n = (x  b) / (x  a) n = LOG[(x  b) / (x  a)] / LOG(u) Hope that helps. I'm not doing it all for you! By the way, it is not possible to find the interest rate directly: "iteration" is required.  

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