9 of 54 Ifanmout ofmoney S $ sput in a bank a count ping an annual interest tant t. murt ofin wei caned affer a year is by definition r.ss The gum S thus becomes afterone year sn+r)SFor instance. ifs-100$and!"7%the sum becomes S. 107 S afer a year 1) If this sum S S is now placed at the same rate r for n years, which final amount does one get? Comenely,which sum in S should one place in an account for n years in onder to get at the end an mount S This smi called the present valueof Is it smaller or larger thn S yeas (+10 nmahumah cally it's clo olns 2) We now consider a loan of amount M granted by a hank to a client who wants to purchase a home mortgage The clien must remburse at the end of each yoar the me amount X during consecutive yeans, to compewsate for the sum M neceived upfront to panchase the home Find a relation betwecn M and the of M by applying the previous formala Simplify the omulia thus obtained (X is called an "amuity s X to he puid each year. Deduce the amount X as a fnctio (44)