# Calculate interest

I'm kinda stuck with the following problem.

I am given the terms in Month, a net-value, a residual value, and a monthly rate. Now my job is to calculate the interest. Usually I am giving the interest and calculate anything else using the following formula:

where $$n$$ is the terms in month, $$R$$ is the monthly rate, $$L$$ is the net-Value, $$RW$$ is the residual value after $$n$$ months. Finally $$q = (1+i)$$, where $$i$$ is the interest.

Any idea how to solve this for $$q$$, i.e. the interest?

You can't derive a formula from this equation to calculate $$q$$ (or $$i$$) directly for all values of $$n$$ given the other variables.
However, you can use the RATE() function in Excel (or a similar function in another electronic spreadsheet program) to find $$i$$. You can also set up a payment schedule similar to the loan amortization table shown here in Excel for a given initial value, monthly payment, residual value, and period and use the Solver add-in or go by trial-and-error to find $$i$$. See this online lease calculator if you would like to double-check your calculations.