Question

3. Suppose you have money invested in a savings monthly. You also make a deposit of D dollars once each month, and you make a withdrawal of P percent of the balance each month. (a) Sketch a compartmental diagram for the amount of money in the account. (b) Write a difference equation (or recurrence relation) for this model (c) Find the fixed points (d) Suppose that r=0.03 and P 0.07 . Find the amount D that you should deposit each month so that the fixed point will be $3,000. account that earns interest rate r (in decimal form)

Answer 1

Page N youvA Date: Cempartmental uagam for. afmone in the account 1lae amouut Let x lt tehe in Hue amount be account t months. J Accoust Ddufkors rrausal x l): aMount Per month eadh montR interes- creedited eachpaanth amount in DIfference equation for (b) ee accouw s xlt) + 9 x LH +D - P z() (1+ -P) x () +D x ( For fixed poluds 2(b+1) - ves P) 4) +D (Dx. えCt) = P-A Kixed Petut Hence

Pa3a No Date: Youv o.o 3 $ 3000 ixed poiut atn These in SubsHtutg we 3000 6.07 -o. o 3 1ao 3o00 X O. O 4 $120