# Calculating interest rate for a payment plan

I really should know this from high school so I'm a bit ashamed to ask... :) I've been offered several cars for lease and want to compare the offered interest rates.

E.g. I have:

Car: Ford Fiesta 1.0T
Lease period: 36 months
Price: 156619 SEK
Residual value: 37589 SEK (30%)
Monthly payment: 3159 SEK


What's the formula to calculate the interest rate I'm being offered here?

Price $P$. Residual value, or the amount for which you can successfully sell the car after $L$ months, $R$. Hence amount you are actually borrowing is effectively $B=P-R$.
Now you are paying a total of $T = L\times M$ where $M$ is the monthly payment. Therefore the percentage difference in the amount you pay versus the amount you borrow is $$I=100\%\times( T-B)/B=100\%\times (LM/(P-R) - 1)$$