The lump sum discount rate calculator is used to calculate the discount rate (i) needed to compound a lump sum from its present value (PV) to a future value (FV) over a given number of periods (n).

# Discount Rate

## Effective Interest Rate for any Time Period

The effective interest rate adjusts the stated nominal rate to allow for the effects of compounding over a specific time period, referred to as the effective period. Different compounding periods earn different amounts of interest and the effective interest rate allows comparisons to be made by converting these to an equivalent rate as if compounding took place once every effective period,

## Effective Annual Rate (EAR)

The effective annual rate adjusts the stated nominal rate to allow for the effects of compounding. Different compounding periods earn different amounts of interest and the effective annual rate allows comparisons to be made by converting these to an equivalent rate as if compounding took place once at the end of the year, hence the alternative name of annual equivalent rate (AER).

## Real Interest Rate Formula

## Periodic to Continuous Interest Rate Formula

## Continuous Compound Interest Formula

## Excel NOMINAL Function

The Excel NOMINAL function is used to calculate the nominal annual rate (i) required to give an effective annual rate (r), allowing for a given number of compounding periods each year (m). The effective rate allows for compounding, whereas the nominal rate does not allow for compounding.

## Nominal Interest Rate Formula

## Effective Interest Rate Formula

## MIRR Formula

The MIRR formula is used to calculate the rate of return for a project taking into account the finance cost (f) of the cash used to fund the project (negative cash flows), and the rate of return (r) on cash from the project (positive cash flows) reinvested elsewhere.

## Excel RATE Function

The Excel RATE function is used to calculate the discount rate (i) in time value of money calculations. For example, it can calculate the interest rate on a loan given the value of the loan, the term and the periodic payments, it can be used to calculate the interest rate earned on a savings account, or the interest rate needed to generate annuity payments from a lump sum investment.

## Excel IRR Function

The Excel IRR function is used to calculate internal rate of return for a range of cash flows in time value of money calculations, and has the syntax IRR (Values, Guess).

Care must be taken when using the Excel IRR function with cash flows that change sign multiple times though out the term of the project, as it can produce meaningless solutions.