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Note: Correct answer to calcolations-based questions will enly be awarded full mark if elearly stated namerical formala (including the left hand side of the equation) is provided. Correst answer nithont ealcalations support nill enly receive a tiny fraction of mark asigned for the question. Question 1(15 marks) a) Asse X generates a porpstual stream of cash flows of $100,000 every 3 months. The relevant imerest tate is 12% coemposided equaricily. How much weald yeo pay to buy Asset X today if the fint payment oscurs right away? (5 marks) b) You are sonsilering depositing 51 million into a bank aceount. After ene year, how much moxe interest en interet will you find in Aecouat (A) that poovides an interet of 12\%. compounded quarterly than Accoant (B) that provides an iacentst of 12% campouded scmaanmully? (s marks) e) The Shaky Finance Led, has aereed to provide a bean to Meena on a "four-for-five" monthly basis. That is for every 54 Meena borrows today, she las so rrpay a toeal or 55 a moneth later What is the true yearly rate of this loan? (5 marks) Qucation 2(20 marks) a) Carter expects of live for 30 yeans moee after his retiremient. He would like to withdraw \$120,600 every year frem his investment account (Aceount A ) to pay for his living expenseb. Caner's invedment acecun (Aesount A) pays 5% interes per year. How mach moecy (a lump-sum) will Carter requird to deposit in Account A at the beginning of his retirement (at age 60 ) to pay for his living expenes if (i) Account A sart to pay increst onc year afts his oxtinemeng? (5 mark) (ii) Account A start to pay interest on the day of his rstirment? (5 marks) Whinf: The weal deposit that Carter made at the beyineing of his retirement it Account A should be the saine as the amsant required to provide for the mombly living expenses during his retirement year.) b) Concinual witt part (aii). Suppose Carter has just had has 35 buirthedy todey and decided to begin lis retirement (exatlyy 25 years from now, at lis age of 60 . To ensure having sufficieat funds to mote his goul, Caricr plans to syart depositing a fived amount at the end of every month to a reticement savings account (Acceunt BH) that pays an interest of 12%, compounded montkly. The fint deposis will be made coday (en his 35 th birthdryj and the bay on his 58 birthdyy. (9) Compute the size of the wonthly deposit into Account is that will allow Carser to meet the financial goal of tis tetirctuent (8 marks) (ii) If Carter is going to make one single (lump-sum) deponit ieno Aceoum B on his 40 birthday instead, how much will that be for him to whicve the pool? (2 marks) John has just purchased an apartment at a price of $5,000,000. He made a down-payment of $2,000,000 and financed the remaining with a 30 -year mortgage at APR 12%, compounded monthly. (a) Determine the size of the fixed month-end payments. ( 5 marks) (b) Calculate the amount John still owes the bank right after the 120th payment was made. ( 5 marks) (c) Calculate the interest payment and the amount of principal paid in the 121st loan repayment. (5 marks) Notet Correct answer to calcelations-bened questions mall only be awarded full mark if clearly stated suacrical formela (iacluding the left-hand slde of the equatioe) is provided. Correct answer without calcalations suppert wint enly receive a tiny fraction of wark assigned for the qucstion. Qucatine 1 in marks] a) Asset X gencrales a perpepal stream of cauk flows ef 5100,000 every 3 months. The relevaet ieserest rate is 12\%, compounded quarterly. How ach would you pay so buy Aset X today if the fint payment occurs right away? (5 marks) b) You are considcring depositing $1 million ints a bunk account. After one year, how much mese interest on interest will you find in Aecwen (A) that provides an intereot of 12% compounded cuaterly than Account (B) that powiles an inierest of 12 fis compousded semiannually? (5 marks) c) The Sharky Finance Lid. has agreed to provide a lowo te Meenar on a Teur-for-five" montbly bauis. That is, fer every $4 Meena botrows loduy, she has to repay a wotal of $5 a eweech later. What is the true yearly rate of this loan'? (5 marks) Qucstion 2(20)marks) a) Carier expects to live for 30 ycars more after his net renent. He would like to withdrans $120,000 every year from his investmetet accoent (Aceount A) to pay for his liviny expenses. Carter's investment account (Accoent A) puys 5% intereat per year. How ansch money (a lump-suma) wall Caner raqurct to deposit in Nccount A at the begiataing of his retircment (at age 6o) to pay fot his lising espenses if (i) Account A start to pey intenct onc ycacafter his rotirgment? (5 marks) (ii) Account A stat to pay interest on the dry. ef Pis netitsencts? (5 marks) [Wiet: The tocal deposit that Carter made at the begines of his retinement in Account A should be the same as the amount requirnd to provide fire the monthly living expenses during his retarement years.] b) Continued with part (aii). Suppose Carter has jeat had list 35 buthulry moday and decided to begin his retarement (exactly) 25 years from sors, at lis age of 60. To ensure having sufficient funds to mect his goal, Carter plans to iturt depositing a fixed an interest of 12 es, compounded moohly. The firs deqeit will be made boday (eo his 35at birthday) and the las in his 5s4 birihayy. (i) Compute the size of the meestly deperit ime Acewont 8 that will allow Caricr io mect the financial goal of has serirenent. (s marks) John has just purchased an apartment at a price of $5,000,000. He made a down-payment of $2,000,000 and financed the remaining with a 30 -year mortgage at APR 12%, compounded monthly. (a) Determine the size of the fixed month-end payments. ( 5 marks) (b) Calculate the amount John still owes the bank right after the 120th payment was made. ( 5 marks) (c) Calculate the interest payment and the amount of principal paid in the 121st loan repayment

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