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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:

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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?

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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.

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  • $\begingroup$ Yeah ok, I thought of this already then I need to use a rather numerical apporach to find the solution thanks! $\endgroup$
    – Michael Von Bargen
    Commented Oct 19, 2021 at 7:20

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