Altering a Lease Calculation to take into account an upfront payment I am trying to find the interest rate of a lease if we know the monthly payment amount but have an advance payment.
I have found a site with part of the calculation we need (Scenario 2 on the link below)
www.efunda.com/formulae/finance/lease_calculator.cfm
This calculation when done with Netwon-Raphson produces the correct result, but doesn't take into account the upfront payment, this seems like a simple calculation but I can't seem to find a way to implement it in the provided calculation.
The output that I am trying to match can be found here.
This calculator should provide you with the example values from Scenario 2. With an Advance Payment of 1 this then pushes up the Interest Rate to 1.792% rather than 1.756%. Putting the advance payment down to 0 will produce the same Interest Rate.
I need to figure out how to adjust the calculation from Scenario 2 to take into account the Advance Payment so it produces the correct result.
To test the Newton-Raphson logic I have been using this.
When the calculation from Scenario 2 is fed into this it seems to produce the correct result so it would be a fast way to test the Newton-Raphson for anyone that wants to attempt this.
Thanks
 A: Close analysis of the payment details reveals one difference - the TCALC calculator demands repayment of the residual, and charges 1 additional term of interest.
TCALC (20,000 in 36 months with advanced payment)

Lease Payment 34  :   \$300.00 :  \$15.76 :   \$284.24 :  \$10,269.75
Lease Payment 35  :   \$300.00 :  \$15.33 : \$284.67 :    \$9,985.08
Lease Residual 1  :   \$10,000.00 : \$14.91 : \$9,985.09 :    (\$0.01)

eFunda (19,700 in 35 months)

33    \$300.00 :  \$283.50 :  \$16.50 :   \$10,568.29
34    \$300.00 :  \$283.93 :  \$16.07 :   \$10,284.36
35    \$300.00 :  \$284.36 :  \$15.64 :   \$10,000.00

You can get the same result from eFunda by using a Loan Amount of $\$19,700$, a Residual of $\$9,985$ and $35$ terms, which gives an Interest Rate of $1.79148\%$.
We therefore require that if the interest rate is $i\%$, then the final value when multiplied by $1+\dfrac{i}{1200}$ gives the residual value, which strikes me as hit and miss, although there might be a way to work it into the formula.
