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
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)
eFunda (19,700 in 35 months)
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.