Question

(2 marks) A person deposits $1000 in a savings account that yields x% interest com- pounded annually (xE {1,2,3, 4, 5, 6,7,8,9}) and the account charges a fee of y dollars that is deducted from the account at the end of each year. (At the end of the year, the bank adds the interest and after that deducts the fee.) To avoid complications involving accounts with negative balances we assume that the interest paid is greater than the fee, that is, 0.0x - 1000 > y. first (a) Let An be the money in the account after n years. The initial value Ao is 1000. Give a recurrence relation for An (b) Using the iteration method for first order recurrences solve the recurrence for An (that is, give a formula for Aj as a function of n)

Answer 1

Soluion Glven data, Rate Deckuckons y dollaus por ye des tt An be the money o the fnfial ofter account eams and Ao lalue the gield an meraAp ytan lnteres af deduction then ydollos Ana 0An- n,:0,1,2. Po: $1000 An- 1DO An:

Wlore uinhe 4eration method ROY 1&t ocler have for An the 40 Solve teccwrence Ao1000 n 1 Ai 100 1000-4 1DO 1+ 1000- 100 IDO eneal for ID00-

Suro of geometic progresions 37 By ం 1000-4 100 00 I004 I00 00y IDOY 1+ 100 lo00- 7 An