# load debkeeprlibrary(debkeepr)

Division and multiplication

One of the more straightforward calculations in bookkeeping isdivision or multiplication of a value to split it among multiplepartners or to calculate costs that are charged at a certain percentageof the value of the goods. For instance, in transaction 18 in thejournal the merchant Randoll Rice purchased 100 pieces of says or woolenserges for £566 13s. 4d. sterling that were sent to Lisbon for a companyin which Rice had a three-fifths part. Transaction 19 calculates thevalue of Rice’s part in the says.

# 19. For Rice's 3/5 part of the 100 says valued at £566.13.4 nr 18tr18<-deb_lsd(566,13,4)tr18*3/5#> <deb_lsd[1]>#> [1] 340:0s:0d#> # Bases: 20s 12d

In transaction 21 expenses for the says are dealt with, including abrokerage charge of 1/8% and a provision charge of 1/3%.

# 21. For brokerage costs in nr 18 and 20 at 1/8% and provision at 1/3%sum(tr18*1/800,tr18*1/300)#> <deb_lsd[1]>#> [1] 2:11s:11.333d#> # Bases: 20s 12d

Interest

Another straightforward calculation is that of interest. Daffornededicated an entire section of his bookkeeping manual to the calculationof interest, providing his readers with a table to calculate interest atdifferent rates for different periods of time. An example in the journalis transaction 87 that assesses interest of 8% on £96 14s. 9d. sterlingover a period of four months. Though the result here would round down to£2 11s. 7d., the journal lists the interest as £2 11s. 8d.

# 87. For £96.14.9 detained upon interest at 8% for 4 monthsdeb_lsd(96,14,9)*0.08*4/12#> <deb_lsd[1]>#> [1] 2:11s:7.12d#> # Bases: 20s 12d

Weights and value of sales/purchases

debkeepr is meant to work with non-decimal currencies,but the ability to change the bases for thesolidus anddenarius units makesdebkeepr types quiteflexible.deb_lsd vectors need not represent pounds,shillings, and pence. They can also be measurements of various sortsthat also adopted a tripartite unit system. An example of this ispresented in the third transaction in the journal that records theweight and value of five barrels of kettles. The weights are given interms of hundredweight, quarters, and pounds. A hundredweight wasequivalent to four quarters, and one quarter equaled 28 pounds. Themeasurements also provided a tare value for the weight of the barrels,which was shown in pounds.

To find the total net weight of the kettles, the gross and tareweights can be found and then subtracted to find the net weight. Thiscan be done by transforming the gross and tare values todeb_lsd vectors with bases of 4 and 28.

# 3. Gross weight(kettles_gross<-deb_lsd(l=c(2,2,2,2,1),                          s=c(3,2,1,0,3),                          d=c(26,18,21,17,5),                          bases=c(4,28)))#> <deb_lsd[5]>#> [1] 2:3s:26d 2:2s:18d 2:1s:21d 2:0s:17d 1:3s:5d#> # Bases: 4s 28d# Tare(kettles_tare<-deb_lsd(l=0,                         s=0,                         d=c(23,21,22,19,17),                         bases=c(4,28)))#> <deb_lsd[5]>#> [1] 0:0s:23d 0:0s:21d 0:0s:22d 0:0s:19d 0:0s:17d#> # Bases: 4s 28d# Net weight(kettles_net<-sum(kettles_gross)-sum(kettles_tare))#> <deb_lsd[1]>#> [1] 11:0s:13d#> # Bases: 4s 28d

Transaction 3 notes that the kettles were valued at £4 19s. perhundredweight. The two values cannot be multiplied, as multiplicationbetween twodeb_lsd vectors is not implemented, nor wouldit be possible to do so since the two vectors have differentbases. Instead, the price can be multiplied by thedecimalized weight created by castingkettles_net to anumeric vector of the correct unit — here, thelibra unit.

# 3. Decimalize hundredweight(kettles_num<-as.numeric(kettles_net))#> [1] 11.11607# Value of the kettles(deb_lsd(4,19,0)*kettles_num)#> <deb_lsd[1]>#> [1] 55:0s:5.893d#> # Bases: 20s 12d

This method of multiplying the price by the decimalized weight of aset of goods can be used in a variety of circumstances. For instance, itis possible to follow the purchase and sale of sugar from Lisbon in thejournal through this method. In transaction 54 from 21 March 1633 thebookkeeper recorded an agreement to purchase ten chests of sugar fromLisbon weighing 51 hundredweight 3 quarters 4 pounds at the price of13d. per pound from James Wilkinson. Because the price is given in termsof the pound unit, thedeb_lsd vector is cast to adeb_decimal vector in terms of the pence ordenarius unit before being cast tonumeric.

# 54. 51 hundredweight 3 quarters 4 pounds of sugar at 13d. per pound# Weight in decimalized poundssugar_lbs<-deb_lsd(51,3,4, bases=c(4,28))%>%deb_as_decimal(unit="d")%>%as.numeric()# Pricedeb_lsd(0,0,13)*sugar_lbs#> <deb_lsd[1]>#> [1] 314:3s:4d#> # Bases: 20s 12d

As an aside, it would also be possible to represent the weight of thesugar, as well as other weights in Dafforne’s journal, as tetrapartitevalues by including the unit of the ton of twenty hundredweight throughthedeb_tetra type. We could manually normalize the value,or usedeb_normalize() with the new set of bases of lengththree. In this case, their is little gained by moving to the use of thedeb_tetra type, but it might be useful if weights werelisted in this tetrapartite form in other places of the account book orby other factors.

# Normalize 51 hundredweight 3 quarters 4 pounds of sugar as tetrapartite valuedeb_tetra(0,51,3,4, bases=c(20,4,28))%>%deb_normalize()#> <deb_tetra[1]>#> [1] 2:11s:3d:4f#> # Bases: 20s 4d 28f

By May, the merchant had found a willing buyer for the sugar at theprice of 14d. per pound in the person of George Pinchback. However, whenthe sugar arrived from Lisbon, there was actually 15 chests weighing 77hundredweight 2 quarters 20 pounds. All of the merchants involved agreedto the same prices. Transactions 102 and 103 record the purchase priceof the sugar and the profits resulting from the 1d. pricedifference.

# 102. 77 hundredweight 2 quarters 20 pounds of sugarsugar_lbs2<-deb_lsd(77,2,20, bases=c(4,28))%>%deb_as_decimal(unit="d")%>%as.numeric()# purchase price of the sugar(sugar_purchase<-deb_lsd(0,0,13)*sugar_lbs2)#> <deb_lsd[1]>#> [1] 471:5s:0d#> # Bases: 20s 12d# 103. profits from the sugardeb_lsd(0,0,1)*sugar_lbs2#> <deb_lsd[1]>#> [1] 36:5s:0d#> # Bases: 20s 12d

To complete the deal, Wilkinson needed to be paid for the sugar.Transaction 105 shows that he was paid in the form of 8 silver barsweighing 1733 ounces that were values at 6s. 7.5d. per ounce. However,the bars had a higher value than the sugar, and so transaction 106 showsWilkinson making a payment to the cash register to even out the paymentsfor the £471 5s. purchase price of the sugar. There is a discrepancy ofone-half of a penny, but Dafforne ignored this.

# 105. Payment for sugar# Value of the 8 silver barsdeb_lsd(0,6,7.5)*1733#> <deb_lsd[1]>#> [1] 574:1s:1.5d#> # Bases: 20s 12d# 106. Value of sugar at 13d. plus payment of cashsum(sugar_purchase,deb_lsd(102,16,1))#> <deb_lsd[1]>#> [1] 574:1s:1d#> # Bases: 20s 12d

Going through the calculations for this purchase and sale of sugarhelps to better understand how Dafforne wanted a merchant to keep hisaccounts. Though no goods or money had changed hands at the time oftransaction 54, Dafforne advised merchants to record any promise ofpayments in an account that he labeled promise reckoning (account 31 indafforne_accounts). Dafforne shows the same being done forthe agreement to sell the sugar. When the goods arrived, the weight ofthe sugar had increased. Therefore, the merchant had to even out the thepromised amounts for the purchase and sale of the sugar at the previousweight, which is done in transactions 107 and 104 respectively, andcalculate the new values as shown above.

Holland guilders and Flemish pounds

Unsurprisingly much of the trade activity that Dafforne placed in hispractice journal occurred in or funneled through Amsterdam and thusinvolved values recorded in guilders, stuivers, and penningen. Guilderspossessed a different base from pounds sterling, and to complicatematters further, the exchange rate between guilders and pounds sterlingoften went through pounds Flemish. Pounds Flemish was tied to guildersat a rate of 6 guilders to £1 Flemish, and Dafforne listed theestablished exchange rate between pounds sterling and pounds Flemish as£1 sterling to 33s. 4d. Flemish. Though Dafforne provides the exchangerate to pounds Flemish, the transactions in the journal proceed frompounds Flemish to pounds sterling, so the inverse rate has to becalculated. Dividing £1 by the rate inverts the rate and has the addedbenefit of coercing the value to numeric, which can be used as themultiplier for the exchange. It may also be useful to know the inverserate expressed as adeb_lsd value, which could be done bycasting the inverse rate fromnumeric todeb_lsd or taking 1 over the originaldeb_lsdrate.

# Rate for sterling to Flemishsterling_to_flemish<-deb_lsd(0,33,4)# Decimalized Flemish to sterling rate# Divide deb_lsd vectors(flemish_to_sterling<-deb_lsd(1,0,0)/sterling_to_flemish)#> [1] 0.6# Numeric methodas.numeric(sterling_to_flemish)^-1#> [1] 0.6# See the rate as a deb_lsd vector1/sterling_to_flemish#> <deb_lsd[1]>#> [1] 0:12s:0d#> # Bases: 20s 12d

Transaction 5 provides a good example of the workflow to transformguilders to pounds sterling. The transaction tells that Jacob Symonsonpossessed 2,290 guilders of the bookkeeper’s capital deriving from acompany that they had together. The transaction specifies that thiscapital was calculated at the general course of 33s. 4d. Flemish. Theexchange involves two steps: from guilders to pounds Flemish at the rateof 6 to 1 and then from pounds Flemish to pounds sterling at the listedexchange rate.

# 5. Guilders to Flemishtr5_guilders<-deb_lsd(2290,0,0, bases=c(20,16))tr5_flemish<-deb_convert_bases(tr5_guilders, to=c(20,12))/6# Flemish to sterlingtr5_flemish*flemish_to_sterling#> <deb_lsd[1]>#> [1] 229:0s:0d#> # Bases: 20s 12d

Transaction 33 presents a slightly more complex example. It involves1,224 guilders 19s. 8d. that Jacob Symonson received through a bill ofexchange at an exchange rate different from the general course. Unlikethe inverted rate for 33s. 4d. Flemish, the given rate of 36s. 10d. doesnot easily reduce itself. It is noteworthy that despite this complexity,Dafforne’s calculation is the same as done here if the pence wererounded at the end of the calculations.

# 33. 1224 guilders 19s. 8d. through bills of exchange# Inverse ratetr33_rate<-deb_lsd(1,0,0)/deb_lsd(0,36,10)# Convert bases and do exchangetr33_guilders<-deb_lsd(1224,19,8, bases=c(20,16))tr33_flemish<-deb_convert_bases(tr33_guilders, to=c(20,12))/6tr33_flemish*tr33_rate#> <deb_lsd[1]>#> [1] 110:17s:1.792d#> # Bases: 20s 12d

A final example for the conversion between guilders and poundssterling is provided by transaction 40, which records the sale of 60Leeds dozens or broadcloths in Amsterdam by Jacob Symonson. Thirtypieces of cloth were sold at 45 guilders 7s. 8d. per piece, and theremaining thirty were sold at 50 guilders per piece. The total proceedsfrom the sales had to be calculated and then converted to poundssterling at the normal rate of 33s. 4d. Flemish.

# 40. Proceeds from the two sales(tr40_sale<-sum(deb_lsd(45,7,8, bases=c(20,16))*30,deb_lsd(50,0,0, bases=c(20,16))*30))#> <deb_lsd[1]>#> [1] 2861:5s:0d#> # Bases: 20s 16d# Sum of proceeds and conversion from guilders to Flemishtr40_flemish<-deb_convert_bases(tr40_sale, to=c(20,12))/6# To sterlingtr40_flemish*flemish_to_sterling#> <deb_lsd[1]>#> [1] 286:2s:6d#> # Bases: 20s 12d

French crowns

Dafforne’s journal contains many transactions with a factor in Rouennamed Jean du Boys who used the French crown of 60 sous as his money ofaccount. The exchange rate between French crowns and pounds sterlingdiffered by transaction, but all were listed in terms of deniers perpound sterling. This rate can be decimalized by casting tonumeric or through a longer process using adeb_decimal vector. Thus, in transaction 20 Jean du Boyswas remitted £2,148 50s. 6d. French crowns at the rate of £1 Frenchcrown to 63d. sterling.

# 20. For £2148 50s. 6d. French crowns at 63d. sterling# Rateas.numeric(deb_lsd(0,0,63))#> [1] 0.2625# or with deb_decimaldeb_decimal(63, unit="d")%>%deb_convert_unit(to="l")%>%as.numeric()#> [1] 0.2625tr20_crowns<-deb_lsd(2148,50,6, bases=c(60,12))deb_convert_bases(tr20_crowns, to=c(20,12))*0.2625#> <deb_lsd[1]>#> [1] 564:1s:5.025d#> # Bases: 20s 12d

A merchant involved in long-distance trade often had to record thevalue of transactions that occurred in currencies that differed from themoney of account used in the account book. Such a situation appeared intransaction 58 in which Jacob Symonson in Amsterdam received a bill ofexchange from Jean du Boys in Rouen that consisted of capital for acompany involving the bookkeeper and Randoll Rice. Jean du Boys sentSymonson £1,140 17s. 8d. French crowns at the rate of 123d. Flemish, andthis transaction was calculated at the rate of 72d. sterling for thepurposes of accounting in terms of pounds sterling. In this case, abookkeeper needed to know the amount of guilders received by Symonson,which was calculated through pounds Flemish, as well as the value inpounds sterling.

# 58. Crowns to Flemish to guilderscrowns_to_flemish<-as.numeric(deb_lsd(0,0,123))tr58_crowns<-deb_lsd(1140,17,8, bases=c(60,12))tr58_flemish<-deb_convert_bases(tr58_crowns,                                  to=c(20,12))*crowns_to_flemishdeb_convert_bases(tr58_flemish, to=c(20,16))*6#> <deb_lsd[1]>#> [1] 3506:8s:1.733d#> # Bases: 20s 16d# Crowns to sterlingcrowns_to_sterling<-as.numeric(deb_lsd(0,0,72))deb_convert_bases(tr58_crowns, to=c(20,12))*crowns_to_sterling#> <deb_lsd[1]>#> [1] 342:1s:9.2d#> # Bases: 20s 12d

Polish florins

The above examples all involved single pounds, shillings, and pencevalues even if multiple values went into the calculation. This is hardlyaccidental. Dafforne advised that every transfer of value betweenaccounts should be listed separately.⁶ However, transactions 64 and 65 present anopportunity to show calculations made on multiple values at the sametime. On 7 April 1634, the bookkeeper sent two bills of exchange toArthur Mumperson in Danzig on behalf of Jacob Symonson. The money ofaccount used by Mumperson in Danzig was the Polish florin of 30 gros andgros of 18 denar, and the exchange rate was again calculated in terms ofpounds Flemish. In this case, both bills of exchange were sent at therate of 232 gros per £1 Flemish, though the calculation requires theinverse rate. There are again a couple of ways to calculate the rate forthe exchange, but here adeb_lsd vector is created with thevalue, the inverse is found, and then this is cast tonumeric. In this example, the Exchange between florins toFlemish to sterling is done using themagrittr pipe(%>%) and the prefix form of the multiplicationoperation.

# 64 and 65. Bills of exchange to Danzig# Rate of 232 gros per £1 Flemishtr64_rate<-as.numeric(1/deb_lsd(0,232,0, bases=c(30,18)))# Convert florins to sterling through pounds Flemish using the pipedeb_lsd(l=c(3987,1907),        s=c(16,26),        d=0,        bases=c(30,18))%>%deb_convert_bases(to=c(20,12))%>%`*`(tr64_rate)%>%`*`(flemish_to_sterling)#> <deb_lsd[2]>#> [1] 309:7s:6.621d 148:0s:5.793d#> # Bases: 20s 12d

Portuguese real

The final currency dealt with in Dafforne’s practice journal is thePortuguese real, which came about from trade conducted by Diego delVarino in Lisbon. The Portuguese real as used in the Dafforne journalpresents a money of account quite different from all others in thejournal. Not only is the base of 1,000 réis to the milréis of a verydifferent magnitude from the pound sterling of 20 shillings, but thereal only has two units instead of the three units of the pounds,shillings, and pence monies of account.debkeepr canaccommodate this type of money of account, but a placeholder value mustbe provided for thedenarius unit, because neither of the twovalues passed tobases can be zero or missing.

The other issue with the real is that the exchange rate is given as400 réis for 5s. sterling, complicating the calculation of the exchangerate. One way to find the ratio is to multiply the réis value by four toget réis equivalent to £1 sterling and then finding the inverse. Anotherway is to multiply the shillings by 2.5 to find shillings per 1 milréis,converting theunit tolibra, and then casting tonumeric.

Transaction 51 shows the purchase of 1,576 pieces of figs by Diegodel Varino for a company with the bookkeeper and Randoll Rice. The figswere purchased for the price of 681 milréis 960 réis with the exchangerate, as noted above, of 400 réis for 5s. sterling.

# 51. purchase of 1576 pieces of figs for 681 milréis 960 réistr51_reis<-deb_lsd(681,960,0, bases=c(1000,12))tr51_converted<-deb_convert_bases(tr51_reis, to=c(20,12))# Method 1: multiply rate of réis by 4 and invert ratetr51_converted/as.numeric(deb_lsd(0,400,0, bases=c(1000,10))*4)#> <deb_lsd[1]>#> [1] 426:4s:6d#> # Bases: 20s 12d# Method 2: multiply rate of shillings by 2.5 and convert to decimalized poundstr51_rate<-deb_decimal(5*2.5,"s")%>%deb_convert_unit(to="l")tr51_converted*as.numeric(tr51_rate)#> <deb_lsd[1]>#> [1] 426:4s:6d#> # Bases: 20s 12d