Compound interest calculation on changing balance for data.table - r

Question

I have a data.table which has a balance. The balance is based on deposits/withdrawals each period. Each period there is an interest rate that should be applied. However I am not able to compound the interest rate to the balances, basically applying the interest rate to the balance and then using the updated balance in the next period to calculate the new value.
Balance_t1 = (0 + Deposit_t1)*(1+Interest_t1)
Balance_t2 = (Balance_t1 + Deposit_t2)*(1+Interest_t2)
Balance_t3 = (Balance_t2 + Deposit_t3)*(1+Interest_t3)
I have the following data.table
dtCash <- data.table(
Deposit = c(100, 100, -300, 0),
Balance = c(100, 200, -100, -100),
Interest=c(0.1, 0.01, 0.2, 0.1)
)
The result would be:
dtCash <- data.table(
Deposit = c(100, 100, -300, 0),
Balance = c(100, 200, -100, -100),
Interest=c(0.1, 0.01, 0.2, 0.1),
BalanceWithInterest = c(110, 212.1, -105.48, -116.028)
)
How do I update and reference the updated Balance column in every period?

Answer 1

It seems like you're looking for a "cumulative sum and product," which I don't know of a way to do in R (other than, for instance, with #dynamo's for loop).
That being said, this can be done efficiently with a relatively simple Rcpp solution:
library(Rcpp)
getBalance <- cppFunction(
"NumericVector getBalance(NumericVector deposit,
NumericVector interest) {
NumericVector result(deposit.size());
double prevResult = 0.0;
for (int i=0; i < deposit.size(); ++i) {
result[i] = (prevResult + deposit[i]) * (1.0 + interest[i]);
prevResult = result[i];
}
return result;
}")
Deposit <- c(100, 100, -300, 0)
Interest <- c(0.1, 0.01, 0.2, 0.1)
getBalance(Deposit, Interest)
# [1] 110.000 212.100 -105.480 -116.028
To give a sense of the efficiency improvements of Rcpp vs. base R:
# Base R solution
f2 = function(Deposit, Interest) {
Balance <- c(0, rep(NA, length(Deposit)))
for (i in 2:length(Balance)) {
Balance[i] = (Balance[i-1] + Deposit[i-1]) * (1+Interest[i-1])
}
return(Balance[-1])
}
set.seed(144)
Deposit <- runif(1000000, -1, 2)
Interest = runif(1000000, 0, 0.05)
system.time(getBalance(Deposit, Interest))
# user system elapsed
# 0.008 0.000 0.008
system.time(f2(Deposit, Interest))
# user system elapsed
# 4.701 0.008 4.730

Answer 2

Not enough rep to comment yet:
Can you give an indication of what data you have at each point/ when you wish to update? Do you wish to calculate, say, balance_after_interest(t) based on interest, balance(t-1) and deposits(t)?

Answer 3

A somewhat messy answer:
library(data.table)
dtCash <- data.table(
Deposit = c(100, 100, -300, 0),
Balance = c(100, 200, -100, -100),
Interest=c(0.1, 0.01, 0.2, 0.1)
)
# Add row for t = 0
dtCash <- rbind(rep(0, ncol(dtCash)), dtCash)
# Add "dummy" column for interest-accrued balance
dtCash$Balance.1 <- c(0, rep(NA, nrow(dtCash)-1))
for ( i in seq(nrow(dtCash))[-1] ) {
dtCash$Balance.1[i] <- (dtCash$Balance.1[i - 1] + dtCash$Deposit[i]) *
(1 + dtCash$Interest[i])
}
dtCash
# Deposit Balance Interest Balance.1
# 1: 0 0 0.00 0.000
# 2: 100 100 0.10 110.000
# 3: 100 200 0.01 212.100
# 4: -300 -100 0.20 -105.480
# 5: 0 -100 0.10 -116.028
Is this what you mean? This isn't super efficient, but it does give you what you are looking for. With some clever re-parameterisation you might be about to work around the explicit loop.
Also, if your problem size is small, you could just as well use data.frame rather than data.table. In this case, the notation would be identical. (And in this case, there is no advantage from using data.table.)

Answer 4

I think you need to pull out the data, work it out with lapply(), and update it. I don't think there's any vector way to do it:
interest<-dtCash[,Interest]
balance<-dtCash[,Balance]
lapply(1:(length(interest)-1), # leave the last entry - nothing to add it to
function(x)
{balance[x+1]<<-balance[x+1]+balance[x]*interest[x]} # remember the double arrow
) # because you're in a function
dtCash[,rollBal:=balance]
Deposit Balance Interest rollBal
1: 100 100 0.10 100.00
2: 100 200 0.01 220.00
3: -300 -100 0.20 -95.70
4: 0 -100 0.10 -138.72