My Math Forum  

Go Back   My Math Forum > Science Forums > Economics

Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance


Reply
 
LinkBack Thread Tools Display Modes
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
idonovan is offline  
 
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:
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.
Denis is offline  
Reply

  My Math Forum > Science Forums > Economics

Tags
annuities, due, leasing, vehicle



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Finance problems (Annuities) help!! Noritaka Economics 19 May 19th, 2014 04:17 AM
Finding the speed of the vehicle sachinrajsharma Algebra 1 April 25th, 2013 11:32 PM
Annuities question stomper123 Economics 2 June 16th, 2012 10:25 PM
How to Calculate these Annuities - Help!? LePrestige Economics 0 August 26th, 2010 02:29 AM
Life annuities Vedmachka Advanced Statistics 1 April 14th, 2008 04:26 AM





Copyright © 2019 My Math Forum. All rights reserved.