Rate function added

README.md

@@ -21,7 +21,7 @@ which are as follows:
 | ppmt                         |  ✅   |   Computes principal payment for a loan|
 | nper                         |  ✅   |    Computes the number of periodic payments|
 | pv                           |  ✅   |   Computes the present value of a payment|
-| rate                         |      |    Computes the rate of interest per period|
+| rate                         |  ✅   |    Computes the rate of interest per period|
 | irr                          |      |    Computes the internal rate of return|
 | npv                          |  ✅   |   Computes the net present value of a series of cash flow|
 | mirr                         |      |    Computes the modified internal rate of return|
@@ -45,9 +45,11 @@ While the numpy-financial package contains a set of elementary financial functio
     + [Example(IPmt-Investment)](#exampleipmt-investment)
   * [PPmt(Principal Payment)](#ppmt)
     + [Example(PPmt-Loan)](#exampleppmt-loan)
-	* [Nper(Number of payments)](#nper)
+  * [Nper(Number of payments)](#nper)
     + [Example(Nper-Loan)](#examplenper-loan)
-
+  * [Rate(Interest Rate)](#rate)
+	+ [Example(Rate-Investment)](#examplerate-investment)
+
  Detailed documentation is available at [godoc](https://godoc.org/github.com/razorpay/go-financial).
 ## Amortisation(Generate Table)  
 
@@ -573,3 +575,66 @@ func main() {
 }
 ```
 [Run on go-playground](https://play.golang.org/p/hm77MTPBGYg)
+
+## Rate  
+
+```go  
+func Rate(pv, fv, pmt decimal.Decimal, nper int64, when paymentperiod.Type, maxIter int64, tolerance, initialGuess decimal.Decimal) (decimal.Decimal, bool) 
+```  
+Params:  
+```text
+pv     : a present value
+fv     : a future value
+pmt    : a (fixed) payment, paid either at the beginning (when =  1)
+         or the end (when = 0) of each period
+nper   : total number of periods to be compounded for
+when   : specification of whether payment is made at the beginning (when = 1)
+         or the end (when = 0) of each period
+maxIter	: total number of iterations for which function should run
+tolerance : tolerance threshold for acceptable result
+initialGuess : an initial guess amount to start from
+``` 
+
+Returns:
+```text
+rate    : a value for the corresponding rate
+valid   : returns true if rate difference is less than the threshold (returns false conversely)
+```
+
+Rate computes the interest rate to ensure a balanced cashflow equation
+
+### Example(Rate-Investment)
+
+If an investment of $2000 is done and an amount of $100 is added at the start of each period, for what periodic interest rate would the invester be able to withdraw $3000 after the end of 4 periods ? (assuming 100 iterations, 1e-6 threshold and 0.1 as initial guessing point)
+
+```go
+package main
+
+import (
+	"fmt"
+	gofinancial "github.com/razorpay/go-financial"
+	"github.com/razorpay/go-financial/enums/paymentperiod"
+	"github.com/shopspring/decimal"
+)
+
+func main() {
+	fv := decimal.NewFromFloat(-3000)
+	pmt := decimal.NewFromFloat(100)
+	pv := decimal.NewFromFloat(2000)
+	when := paymentperiod.BEGINNING
+	nper := decimal.NewFromInt(4)
+	maxIter := 100
+	tolerance := decimal.NewFromFloat(1e-6)
+	initialGuess := decimal.NewFromFloat(0.1),
+
+	rate, ok := gofinancial.Rate(pv, fv, pmt, nper, when, maxIter, tolerance, initialGuess)
+	if ok {
+		fmt.Printf("rate:%v ", rate)
+	} else {
+		fmt.Printf("NaN")
+	}
+	// Output:
+	// rate: 0.06106257989825202
+}
+```
+[Run on go-playground](https://play.golang.org/p/9khVcHwjkh5)

reducing_utils.go

@@ -290,3 +290,82 @@ func Npv(rate decimal.Decimal, values []decimal.Decimal) decimal.Decimal {
 	}
 	return internalNpv
 }
+
+/*
+This function computs the ratio that is used to find a single value that sets the non-liner equation to zero
+
+Params:
+ nper 	: number of compounding periods
+ pmt	: a (fixed) payment, paid either
+	  	  at the beginning (when = 1) or the end (when = 0) of each period
+ pv		: a present value
+ fv		: a future value
+ when 	: specification of whether payment is made
+		  at the beginning (when = 1) or the end (when = 0) of each period
+ curRate: the rate compounded once per period rate
+*/
+func getRateRatio(pv, fv, pmt, curRate decimal.Decimal, nper int64, when paymentperiod.Type) decimal.Decimal {
+	oneInDecimal := decimal.NewFromInt(1)
+	whenInDecimal := decimal.NewFromInt(when.Value())
+	nperInDecimal := decimal.NewFromInt(nper)
+
+	f0 := curRate.Add(oneInDecimal).Pow(decimal.NewFromInt(nper)) // f0 := math.Pow((1 + curRate), float64(nper))
+	f1 := f0.Div(curRate.Add(oneInDecimal))                       // f1 := f0 / (1 + curRate)
+
+	yP0 := pv.Mul(f0)
+	yP1 := pmt.Mul(oneInDecimal.Add(curRate.Mul(whenInDecimal))).Mul(f0.Sub(oneInDecimal)).Div(curRate)
+	y := fv.Add(yP0).Add(yP1) // y := fv + pv*f0 + pmt*(1.0+curRate*when.Value())*(f0-1)/curRate
+
+	derivativeP0 := nperInDecimal.Mul(f1).Mul(pv)
+	derivativeP1 := pmt.Mul(whenInDecimal).Mul(f0.Sub(oneInDecimal)).Div(curRate)
+	derivativeP2s0 := oneInDecimal.Add(curRate.Mul(whenInDecimal))
+	derivativeP2s1 := ((curRate.Mul((nperInDecimal)).Mul(f1)).Sub(f0).Add(oneInDecimal)).Div(curRate.Mul(curRate))
+	derivativeP2 := derivativeP2s0.Mul(derivativeP2s1)
+	derivative := derivativeP0.Add(derivativeP1).Add(derivativeP2)
+	// derivative := (float64(nper) * f1 * pv) + (pmt * ((when.Value() * (f0 - 1) / curRate) + ((1.0 + curRate*when.Value()) * ((curRate*float64(nper)*f1 - f0 + 1) / (curRate * curRate)))))
+
+	return y.Div(derivative)
+}
+
+/*
+Rate computes the Interest rate per period by running Newton Rapson to find an approximate value for:
+
+y = fv + pv*(1+rate)**nper + pmt*(1+rate*when)/rate*((1+rate)**nper-1)
+(0 - y_previous) /(rate - rate_previous) = dy/drate {derivative of y w.r.t. rate}
+
+
+Params:
+ nper 	: number of compounding periods
+ pmt	: a (fixed) payment, paid either
+	  	  at the beginning (when = 1) or the end (when = 0) of each period
+ pv		: a present value
+ fv		: a future value
+ when 	: specification of whether payment is made
+		  at the beginning (when = 1) or the end (when = 0) of each period
+ maxIter : total number of iterations to perform calculation
+ tolerance : accept result only if the difference in iteration values is less than the tolerance provided
+ initialGuess : an initial point to start approximating from
+References:
+	Wheeler, D. A., E. Rathke, and R. Weir (Eds.) (2009, May). Open Document
+    Format for Office Applications (OpenDocument)v1.2, Part 2: Recalculated
+    Formula (OpenFormula) Format - Annotated Version, Pre-Draft 12.
+    Organization for the Advancement of Structured Information Standards
+    (OASIS). Billerica, MA, USA. [ODT Document]. Available:
+    http://www.oasis-open.org/committees/documents.php?wg_abbrev=office-formula
+    OpenDocument-formula-20090508.odt
+*/
+
+func Rate(pv, fv, pmt decimal.Decimal, nper int64, when paymentperiod.Type, maxIter int64, tolerance, initialGuess decimal.Decimal) (decimal.Decimal, bool) {
+	var nextIterRate, currentIterRate decimal.Decimal = initialGuess, initialGuess
+
+	for iter := int64(0); iter < maxIter; iter++ {
+		currentIterRate = nextIterRate
+		nextIterRate = currentIterRate.Sub(getRateRatio(pv, fv, pmt, currentIterRate, nper, when))
+	}
+
+	if nextIterRate.Sub(currentIterRate).Abs().GreaterThan(tolerance) {
+		return nextIterRate, false
+	}
+
+	return nextIterRate, true
+}

reducing_utils_test.go

@@ -355,3 +355,70 @@ func Test_Nper(t *testing.T) {
 		})
 	}
 }
+
+func Test_Rate(t *testing.T) {
+	type args struct {
+		pv           decimal.Decimal
+		fv           decimal.Decimal
+		pmt          decimal.Decimal
+		nper         int64
+		when         paymentperiod.Type
+		maxIter      int64
+		tolerance    decimal.Decimal
+		initialGuess decimal.Decimal
+	}
+	tests := []struct {
+		name     string
+		args     args
+		want     decimal.Decimal
+		validity bool
+	}{
+		{
+			name: "success", args: args{
+				pv:           decimal.NewFromInt(2000),
+				fv:           decimal.NewFromInt(-3000),
+				pmt:          decimal.NewFromInt(100),
+				nper:         4,
+				when:         paymentperiod.BEGINNING,
+				maxIter:      100,
+				tolerance:    decimal.NewFromFloat(1e-7),
+				initialGuess: decimal.NewFromFloat(0.1),
+			},
+			want:     decimal.NewFromFloat(0.06106257989825202),
+			validity: true,
+		}, {
+			name: "success", args: args{
+				pv:           decimal.NewFromInt(-3000),
+				fv:           decimal.NewFromInt(1000),
+				pmt:          decimal.NewFromInt(500),
+				nper:         2,
+				when:         paymentperiod.BEGINNING,
+				maxIter:      100,
+				tolerance:    decimal.NewFromFloat(1e-7),
+				initialGuess: decimal.NewFromFloat(0.1),
+			},
+			want:     decimal.NewFromFloat(-0.25968757625671507),
+			validity: true,
+		}, {
+			name: "failure", args: args{
+				pv:           decimal.NewFromInt(3000),
+				fv:           decimal.NewFromInt(1000),
+				pmt:          decimal.NewFromInt(100),
+				nper:         2,
+				when:         paymentperiod.BEGINNING,
+				maxIter:      100,
+				tolerance:    decimal.NewFromFloat(1e-7),
+				initialGuess: decimal.NewFromFloat(0.1),
+			},
+			want:     decimal.NewFromFloat(0.4907342754506849),
+			validity: false,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			if got, isValid := Rate(tt.args.pv, tt.args.fv, tt.args.pmt, tt.args.nper, tt.args.when, tt.args.maxIter, tt.args.tolerance, tt.args.initialGuess); isValid != tt.validity || isAlmostEqual(got, tt.want, decimal.NewFromFloat(precision)) != nil {
+				t.Errorf("Rate returned (%v,%v), wanted (%v,%v)", got, isValid, tt.want, tt.validity)
+			}
+		})
+	}
+}