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The internal rate of return of an investment made at irregular intervals is the constant rate of return which would yield the equivalent value.

For example, suppose you purchased $1000 in a stock on January 15, then $2500 on February 8 and finally another $1000 on April 17. The value of the stock on August 24 is $5050. The internal rate of return could be computed by:

```
var xirr = require('xirr');
var rate = xirr([
{amount: -1000, when: new Date(2016, 0, 15)},
{amount: -2500, when: new Date(2016, 1, 8)},
{amount: -1000, when: new Date(2016, 3, 17)},
{amount: 5050, when: new Date(2016, 7, 24)},
]);
console.log(rate); // Prints 0.2504234710540838
```

This means annualized rate of return is 25.04%. That is, an equivalent investment would be a savings account of with an interest rate of 25.04%. (And if you happen to know of such a savings account, please let the author know immediately.)

This calculation can be used to compare disparate investments.

Given a sequence of transactions, computes the internal rate of return.

**Parameters**:

`transations`

: an array of objects with the following properties:`amount`

: the amount of the transaction`when`

: the Date when the transaction occurred

`options`

: Options to pass directly to the underlying Newton's method implementation,`newton-raphson-method`

**Returns**: the annualized internal rate of return as a decimal in [-1,∞)

**Throws**:

- Error:
- when the
`amount`

s of the transactions are all the same sign - when there are fewer than two transactions
- when the transactions all occur on the same day (time is ignored)
- when the
`newton-raphson-method`

fails to converge

- when the

To compute the irregular rate of return, you must find the constant rate of return which yields a present value of zero over the set of transactions. The present value of a transaction is determined by the formula `A(1+r)`

, where ^{Y}`A`

is the `amount`

, `Y`

is the duration of the investment represented by the transaction in years and `r`

is the rate to solve for. The sum of the present values is the function for which we need to find the zero.

To find the zero of a function, we use Newton's method as implemented by the `newton-raphson-method`

module. To use Newton's method, we need the derivative of the present value with respect to `r`

. Fortunately this is easily determined using the power rule. The derivative is the sum of the terms `AY(1+r)`

for which ^{Y-1}`Y`

is not zero.

I had a very elegant proof of the above but unfortunately the margin is too small to contain it.

- package on npmhttps://npmjs.com/package/xirr
- licenseMIT

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