Solving for Interest Rates in a Loan or Lease Cash Flow

Summary

The document considers how to recover a monthly interest rate from a known term, net value, and residual value when the usual payment relationship is expressed using the rate factor q = 1 + i. Its answer says that q or i cannot generally be isolated in a direct formula for every possible term length and set of inputs.

Instead, it recommends numerical rate finding: use a spreadsheet RATE function, construct a payment schedule and use spreadsheet Solver, or adjust the rate by trial and error until the cash flows match. These methods provide practical ways to solve the implied-rate problem, but the document does not show the underlying equation, explain convergence or input constraints, or compare solver approaches. The example is framed around financing or lease calculations rather than a trading strategy, though the general lesson is that some cash-flow rates require numerical solving.

Key ideas

• The implied interest rate may not have a direct algebraic solution for arbitrary term lengths and inputs.
• A spreadsheet RATE function can solve for the rate from a financing cash-flow setup.
• A payment schedule paired with Solver or trial and error is an alternative numerical approach.
• The answer gives practical methods but does not discuss convergence, constraints, or a specific worked calculation.

Tags

# Calculate interest


# 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?

## Answer by Alper (score 3, accepted)

https://quant.stackexchange.com/a/68426

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.