compute compounding interest with an actual formula

ledger/predict.go

@@ -3,6 +3,7 @@ package ledger
 import (
 	"fmt"
 	"maps"
+	"math"
 	"regexp"
 	"slices"
 	"sort"
@@ -159,27 +160,42 @@ func BPIsWithFixedGrowthPrediction(bpis BPIs, window time.Duration, pattern stri
 func RegisterWithCompoundingInterestPrediction(reg Register, window time.Duration, pattern string, apy float64) (Register, error) {
 	lastBalances := make(Balances)
 	p := regexp.MustCompile(pattern)
-	for _, date := range reg.Dates() {
+	for _, d := range reg.Dates() {
-		for name := range reg[date] {
+		if t, _ := dateToTime(d); time.Now().Before(t) {
+			continue
+		}
+		for name := range reg[d] {
 			if p.MatchString(name) {
-				lastBalances[name] = reg[date][name]
+				lastBalances[name] = reg[d][name]
 			}
 		}
 	}
 
+	predictedTimes := predictionTimes(window)
 	result := maps.Clone(reg)
-	for _, predictionTime := range predictionTimes(window) {
+	for _, predictionTime := range predictedTimes {
 		k := predictionTime.Format("2006-01")
 		if _, ok := result[k]; !ok {
 			result[k] = make(Balances)
 		}
-		for name, balance := range lastBalances {
+		for k2, v2 := range lastBalances {
-			balance2 := maps.Clone(balance)
+			if _, ok := result[k][k2]; !ok {
-			for k := range balance2 {
+				result[k][k2] = maps.Clone(v2)
-				balance2[k] *= 1.0 + (apy / 12)
+			}
+		}
+	}
+
+	for _, predictionTime := range predictedTimes {
+		k := predictionTime.Format("2006-01")
+		for name := range lastBalances {
+			for currency := range result[k][name] {
+				// A = P(1 + r/n)**nt
+				p := result[k][name][currency]
+				r := apy
+				n := 12.0
+				t := float64(predictionTime.Sub(time.Now()) / (time.Hour * 24 * 365))
+				result[k][name][currency] = p * math.Pow(1.0+(r/n), n*t)
 			}
-			result[k][name] = balance2
-			lastBalances[name] = balance2
 		}
 	}