Points to Remember. Financial Mathematics, Ch-15. Example: Convert: (a) US$185 to Singapore dollars (b) S$5000 to Japanese yen.

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1 Foeign Exchange: Points to Remembe Financial Mathematics, Ch-5 Example: Convet: (a) US$85 to Singapoe dollas (b) S$5000 to Japanese yen. (a)the bank will buy US dollas at US$ = S$.693 US$ 85 = 85 x S$.693 = S$33.2 (coect to neaest cent) (b)the bank will sell Japanese yen at Y = S$.200 Y = S$.200 S$.200 = Y S$ = Y.200 S$ 5000 = 5000 Y = Y 3523 (coect to the neaest Y).200 Commission on Cuency Exchange: The commission could be calculated using a fixed pecentage o the buy/sell values. Example: A banke changes South Afican and to othe cuencies at a fixed commission of.5%. Wendy wishes to convet R800 to ubles whee R buys 3.86 Russian ubles. Commission = R800 x.5% = R800 x 0.05 = R2 Wendy eceives = = 788 x 3.86 ubles = 302 ubles. Example: A cuency exchange sevice exchanges euo fo Japanese yen with the buy ate 35.69, and sell ate Cedic wishes to exchange 800 euos fo yen. Cedic eceives 800 x yen = yen.{using the selling ate as the bank is selling cuence} Cedic eceives 779 {using the buying ate as the bank is buying cuency} The esultant commission is = 2.

2 Tavelles Cheques: Usually banks who povide Tavelles cheques chage % of the value of the cheques when they issued i.e., multiply by.0. Example: You want to buy 2000 UK pounds woth of tavelles cheques. What will it cost in Austalian dollas, if AUD = pounds? 2000 Cost = AUD. Simple inteest, S.I = P Cn t o I = whee S.I/I, is the simple inteest P/C, is the pincipal/capital (amount boowed), is the ate of inteest pe annum as a pecentage t, is the time (o length) of the loan, is always expessed in yeas. Example: Calculate the simple inteest on a loan of $8000 at a ate of 7% p.a. ove 8months. S.I = = = $80. Use Calculato: Menu TVM Simple inteest, n= (must be in days) I% = 7 PV (pesent value) = 8000 (enteed as a negative value) SI = $80. Example: How much is boowed if a ate of 6.5% p.a. simple inteest esults in an inteest chage of $3900 afte 5 yeas? = P 5, Use calculato : Menu equa solve 3900 = x Solve = Example: If you wanted to ean $ 6000 in inteest on a yea loan of $ 8000, what ate of simple inteest would you need to chage? 6000 = 8000 Use calculato : Menu equa solve 6000 = 8000 x. Solve = % = 8.33%. Amount with simple inteest: A = P + S.I 2

3 Calculating Repayments fo Simple Inteest Loans: Amount with simple int eest( total to be epaid) P S Regula payment =, numbe of epayments nt Whee, n = numbe of times the inteest is added pe yea & t = yeas Example: Calculate the monthly epayments on a loan of $ at 8% p.a. Flat ate ove 6 yeas. P S nt $72.78 Compound inteest: The total inteest eaned = the final balance the initial capital. C.I = A P Compound inteest is a method of calculating inteest in which the inteest is added to the capital each peiod, i.e., paid inteest on the inteest. Diffeent compounding peiods: Half yealy ( two times pe yea) Quately ( fou times pe yea) Monthly ( 2 times pe yea) Daily ( 365/366 times pe yea) % Amount with Compound Inteest: A = P o P k k Whee: A is the futue value(o final balance/total amount) C is the pesent value o capital( the amount oiginally invested) is the inteest ate pe yea n is the numbe of yeas k is the numbe of compound inteest in a yea Example: calculate the final balance of a $5 000 investment at.25% p.a. whee inteest is compounded monthly fo five yeas A = 5000 o 5000 = $ Use calculato: Menu TVM Compound inteest, n= 2 5,(numbe of time peiods) 2 kn 5 kn 3

4 I% =.25(inteest ate pe yea) Pesent value (pincipal) PV = 5000 (enteed as a negative value.) PMT = 0 Futue value (amount) FV = x Numbe of payments pe yea P/Y (numbe of times the inteest is added pe yea) = 2 Numbe of compounding peiods pe yea C/Y (numbe of times the inteest is added pe yea) = 2 Pess FV = $ Example: How much does Halena need to deposit into an account to collect $ at the end of 3 yeas if the account is paying 5.2% p.a. compounded quately? = 5.2 P = $ Use calculato: Method - Menu equa solve, X = x Method - 2 Menu TVM Compound inteest, n= 3, I% = 5.2, PV = x, PMT = 0, FV = 50000, P/Y =, C/Y = Pess PV = $ Thus, $ needs to be deposited. Example: Fo how long must Magnus invest $000 at 6.5% p.a. compounded half-yealy fo it to amount to $0 000? 2 t = 000 = $ Using solve, t =.3.5 yeas (ounding to next half yea)

5 Altenatively: Menu TVM Compound inteest, n= x, I% = 6.5 PV = 000, PMT = 0, FV = 00, P/Y = 2, C/Y = 2 Pess n = 28.9.Thus, 29 half-yeas ae equied, o.5 yeas =.339 = 2 Note: when using a TVM solve, we find the numbe of compounding peiods and need to convet to the time units equied. The effective inteest ate on an investment : The effective ate is the equivalent annualized ate o equivalent inteest ate compounded annually. To covet a nominal compound ate to an effective ate: i c Whee is effective ate i is the ate pe compound inteest peiod c is the numbe of compound peiods pe annum. Example: Which is the bette ate offeed: % p.a. compounded monthly o.2% p.a. compounded quately? Given i = 2 c 0.333, c = 2 Given i =.2 =.05, c = c i i (.00333) 2 = (.005) the effective ate is.07% p.a the effective ate is.27% p.a The bette ate fo an investment is.2% p.a. compounded quately. Calculato convesion of Nominal ate to effective ate: Menu TVM Convesion n = 2 & I = EFF =.07 Depeciation (decease) is the loss in value of an item ove time. 5

6 In ode to decease an amount by 20%, multiply the amount by 0.8. Example: A photocopie was puchased fo $ 2500 and depeciated at 5% each yea. Find its value afte five yeas. A = 2500 (0.85) 5 = The depeciation fomula: A = P Whee A is the futue value afte n time peiods C is the oiginal puchase pice is the depeciation ate pe peiod and is negative n is the numbe of peiods Example: An industial dishwashe was puchased fo $200 and depeciated at 5% each yea. a. Find its value afte six yeas b. by how much did it depeciate? n a. A = P whee c = 200, = 5, n = 6 A = 200 ( 0.5) 6 = 200 (0.85) so, afte 6 yeas the value is $905.6 b. Depeciation = $200 $905.6 = $9.8 Example: A vending machine bought fo $5 000 is sold 3 yeas late fo $950. Calculate its annual ate of depeciation. Fomula A = 950, C = 5000, n = 3 A = P 950 = 5000 t (using solve) So, the annual ate of depeciation is.0%. Gaphics calculato solution: TVM N = 3, PV = 5000, PMT = 0, FV = 950, P/Y =, C/Y =. I =.0025 Thus, the annual depeciation ate is.0%. n 6

7 Pesonal loans: Total epayments = monthly epayment numbe of months Inteest = total epayments amount boowed Outstanding balance = pevious balance + inteest epayment Example: Raphael takes out a pesonal loan fo $2000 to go oveseas and epays it ove 5 yeas. The monthly epayment fo the loan is $267. Inteest is calculated at 2% p.a.(i.e., % pe month). Calculate the total epayments, inteest chaged and outstanding balance of the loan afte 2 months. Total epayments = $ = $ 6020 Inteest = $ 6020 $ 2000 = $ 020 Outstanding balance: use calculato: Menu ecu Type na n a n (.0) 267. Thus, a n+ = a n (.0) 267. set stat End 3 a EXE Tabl n + a n Thus, the outstanding balance afte 2 months is $ Gaphics calculato solution fo monthly epayments: TVM n = 60, I = 2, PV = 2000, FV = 0, P/Y = 2 PMT = The effect of inflation: ( incease) In ode to incease an amount by 9%, multiply the amount by.09. Example: $00 is deposited in a fixed tem account fo a 3 yeas. Inflation inceases at 2.5% p.a. on a compound basis. $ 00 (.025) 3 = $ Bibliogaphy: Coad Mal; Glen Whiffen, Majut Maenpaa, Mak Humphies, James Foley, Michael Haese and Sanda Haese. Mathematics fo the intenational student Mathematical Studies Sl, Second edition. Haese Hais Publications, Austalia, o0o--- 7