My Math Forum Annuities due vehicle leasing

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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
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Re: Annuities due vehicle leasing

Quote:
 Originally Posted by idonovan 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
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
The payment calculation formula is: P = Ai / (1 - v) where v = 1 / (1 + i)^n
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.

 Tags annuities, due, leasing, vehicle

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