100, , 000 (180 / 365) ln

Transcription

1 1. Diana dcids to purchas a US Trasury Bill for 95,000. Th Trasury Bill maturs in 180 days for 100,000. a. Calculat th quotd rat on this Trasury Bill. Quotd Rat = 360 Amount of Intrst Numbr of Days Maturity Valu , , 000 b. Calculat th annual ffctiv intrst rat th Diana will actually arn. 180/365 ()(1 i) 100, / , i i c. Calculat th continuously compoundd intrst rat th Diana will arn. (180/365) () 100, 000 (180/365) 100, , 000 (180 / 365) ln , 000 ln

2 2. Anis dcids to purchas a Govrnmnt of Canada Trasury Bill for 95,000. Th Trasury Bill maturs in 180 days for 100,000. a. Calculat th quotd rat on this Trasury Bill. Quotd Rat = 365 Amount of Intrst Numbr of Days Purchas Pric , b. Calculat th annual ffctiv intrst rat th Anis will actually arn. 180/365 ()(1 i) 100, / , i i c. Calculat th continuously compoundd intrst rat th Anis will arn. (180/365) () 100, 000 (180/365) 100, , 000 (180 / 365) ln , 000 ln

3 3. David buys a US Trasury Bill with a quotd rat of 8.25%. Th Bill maturs in 120 days for 10,000. Calculat th pric that David pays for th Trasury Bill. Quotd Rat = 360 Amount of Intrst Numbr of Days Maturity Valu , 000 Pric , , 000 Pric (0.0825) (10, 000) Pric 10, 000 (0.0825) (10, 000)

4 4. Lily buys a Govrnmnt of Canada Trasury Bill with a quotd rat of 8.25%. Th Trasury Bill maturs in 45 days for 10,000. Calculat th pric that Lily pays for th Trasury Bill. Quotd Rat = 365 Amount of Intrst Numbr of Days Purchas Pric , 000 Pric Pric 45 10, 000 Pric (0.0825) (Pric) , 000 Pric (0.0825) (Pric) 10, 000 Pric (0.0825) 365

5 5. Noah buys a US Trasury Bill that maturs for 50,000 in 150 days. Noah will arn an annual ffctiv intrst rat on his invstmnt of 6.5%. Calculat th quotd rat on this Trasury Bill. 150/365 (Pric)(1.065) 50, , 000 Pric 48, /365 (1.065) Quotd Rat = 360 Amount of Intrst Numbr of Days Maturity Valu , , , 000

6 6. Th intrst rat that Andrson Bank wants to rciv on a fiv yar loan in ordr to dfrrd consumption is an annual rat of 5% compoundd continuously. For fiv yar loans, th prcntag of loans that will dfault is 0.7%. For th loans whr thr ar dfaults, Andrson Bank will b abl to rcovr 30% of th amount owd aftr fiv yars. Calculat th crdit sprad calculatd as an annual rat compoundd continuously that Andrson Bank nds to charg. Andrson wants to arn an intrst rat that will compnsat hr for dfrral of comsumption and th cost of dfaults. Th annual rat for dfrral of comsumption is 0.05 compoundd continuously. Th annual cost of dfaults is compoundd continuously. Thrfor, th rturn that Andrson wants to arn if thr wr no dfaults would b Th rturn ncssary givn th dfaults is s s Assuming that 1 is borrowd, th amount to b rpaid prior to th cost of dfaults would b (5)(0.05) 5(0.05 s ). If you includ th cost for dfault, thn th amount to b rpaid would b. s s ( ) (0.007)(0.30) 5(0.05 ) 5(0.05 ) 5(0.05) (0.007)(0.30) (0.05 s) 5(0.05) 5(0.05 s) 5(0.05 s ) 5(0.05) (0.007)(0.30) ln( ) 5(0.05 s) ln( ) s

7 7. On tn yar loans, Liu Loan Company wants to rciv an annual rat of 4.5% compoundd continuously bfor taking into account dfaults. This is quivalnt to th rat dsird in ordr to dfr consumption. Whn taking into account xpctd dfaults and rcovry on thos dfaults, Liu chargs an annual rat of 4.55% compoundd continuously. For ths tn yar loans, Liu blivs that 1.2% of th loans will dfault. Furthr, Liu xpcts th loans which dfault will pay X% of th amount owd at th nd of 10 yars. Dtrmin X. Liu wants to arn an intrst rat that will compnsat hr for dfrral of comsumption and th cost of dfaults. Th annual rat for dfrral of comsumption is compoundd continuously so Liu wants to arn if thr ar no dfaults. Th rturn ncssary givn th dfaults is Assuming that 1 is borrowd, th amount to b rpaid prior to th cost of dfaults would b (10)(0.045). (10)(0.0455) If you includ th cost for dfault, thn th amount to b rpaid would b. ( ) (0.012)(rcovry) (10)(0.0455) (10)(0.0455) (10)(0.045) (0.012)(rcovry) (10)(0.0455) (10)(0.045) (10)(0.0455) (10)(0.045) (10)(0.0455) rcovry (10)(0.0455) (0.012)

8 8. Th Dakota Bank maks loans fiv yar loans for collg studnts. Dakota wants to rciv an annual intrst rat 3.2% compoundd continuously without taking into account dfaults and inflation. Dakota knows that inflation for th nxt fiv yars will b at an annual rat of 2.7% compoundd continuously. Collg studnts hav a high dfault rat. Dakota blivs that 4.2% of th studnts will dfault on th loan at th nd of 5 yars. Sh also blivs that sh will b abl to rcovr 45% of th amount owd on dfaults. a. Calculat th crdit sprad that Dakota nds to charg as an annual rat compoundd continuously. Dakota wants to arn an intrst rat that will compnsat hr for dfrral of comsumption, inflation, and th cost of dfaults. Th annual rat for dfrral of comsumption is compoundd continuously. Th annual inflation is compoundd continuously. Th annual cost of dfaults is s compoundd continuously. Thrfor, th rturn that Dakota wants to arn if thr wr no dfaults would b Th rturn ncssary givn th dfaults is s s Assuming that 1 is borrowd, th amount to b rpaid prior to th cost of dfaults would b (5)(0.059) 5(0.059 s ). If you includ th cost for dfault, thn th amount to b rpaid would b. ( ) (0.042)(0.45) (5)(0.059 s) (5)(0.059 s) (5)(0.059) (0.042)(0.45) (5)(0.059 s ) (5)(0.059) (5)( s ) (5)(0.059 s ) (5)(0.059) (0.042)(0.45) ln( ) (5)(0.059 s) ln( ) s

9 b. Calculat th total annual intrst rat compoundd continuously that Dakota should charg for th loans including th componnts for dfault and inflation. Dakota wants to arn an intrst rat that will compnsat hr for dfrral of consumption, inflation, and th cost of dfaults. Th annual rat for dfrral of comsumption is compoundd continuously. Th annual inflation is compoundd continuously. Th annual cost of dfaults is compoundd continuously. Thrfor, th rturn ncssary givn th dfaults is c. Sammi borrows 32,000 from Dakota to b rpaid at th nd of fiv yars. Calculat th amount that Sammi will nd to rpay at th nd of fiv yars. If w carry all th dcimal placs from part a, thn our intrst rat is (5)( ) (32, 000) 43,996.36

10 9. Portr maks thr yar loans which includ inflation protction. Th annual intrst rat compoundd continuously that must b paid is 3.2% plus th rat of inflation. Th US govrnmnt borrows 100,000 for thr yars from Portr. Th actual annual inflation rat during th first yar was 2.4% compoundd continuously. Th actual annual inflation rats for th scond and third yars rspctivly was 2.8% and 4.2% compoundd continuously. Th US govrnmnt is considrd a risk fr borrowr which mans thr is no chanc of dfault. a. Calculat th amount that th US govrnmnt will ow at th nd of thr yars. Th first yar, th govrnmnt will ow compoundd continuously. Th scond yar, th govrnmnt will ow compoundd continuously. Th third yar, th govrnmnt will ow compoundd continuously Amount Owd = 100, , , b. Calculat th annual Ral Intrst Rat compoundd continuously. Th Ral Intrst Rat compoundd continuously is th rat for dfrrd consumption compoundd continuously lss th charg for inflation protction. This is th intrst rat compoundd continuously on an inflation protctd invstmnt whr thr is no dfault risk. Thrfor, for this loan, th Ral Intrst Rat compoundd continuously is c. Th annual intrst rat compoundd continuously that Portr wants to arn to dfr consumption is 3.5%. What is th annual cost compoundd continuously of inflation protction. Th Ral Intrst Rat compoundd continuously is th rat for dfrrd consumption compoundd continuously lss th charg for inflation protction. This is th intrst rat compoundd continuously on an inflation protctd invstmnt whr thr is no dfault risk. Thrfor, for this loan, th Ral Intrst Rat compoundd continuously is Th rat for dfrral of consumption is givn as Thrfor, th charg for inflation protction must b

11 10. Nick maks a svn yar loan to th Govrnmnt of Canada. Th Govrnmnt of Canada is considrd a risk fr borrowr with no risk of dfault. Th amount of th loan is 70,000. Nick wants to arn an annual rat of 3.87% compoundd continuously for dfrring consumption. Nick also xpcts an annual inflation rat of 2.13% compoundd continuously ovr th nxt svn yars. Th Govrnmnt of Canada has agrd to rpay 108, at th nd of svn yars. a. Calculat th cost that Nick is charging for th uncrtainty of th inflation rat. Exprss your answr as an annual rat compoundd continuously. Th total intrst rat rflcts th following four componnts: Rat for dfrrd consumption; Cost of dfaults; Rat for xpctd inflation; and Charg for inflation risk; For this loan, th total annual intrst rat compoundd continuously is 108, ln 70, ,000 =108,418.12==> Th rat for dfrrd consumption is 3.87% compoundd continuously. Th cost of dfaults is zro sinc thr ar no dfaults. Th rat for xpctd inflation is 2.13% compoundd continuously. Thrfor, th annual charg for inflation risk compoundd continuously is b. Calculat th Nominal Intrst Rat that Nick is arning xprssd as an annual rat compoundd continuously. Th Nominal Intrst Rat is total annual intrst rat compoundd continuously which is

12 Answrs 1. a b c % a b c a b c. 43, Assums that you carry all dcimals for th ntir calculation. If you round you will gt a slightly diffrnt answr which could diffr by as much as a. 120, b c a b