Practice section 17 of 17

A grain facility holds $10000$ bushels at the end of December 2013. Insurance pay-outs purchase extra grain, increasing the stock by $2\%$ before the end of every month.

(a) Find the stock at the end of December 2014. [1]

(b) During January–December 2014 the facility supplies x bushels to a laboratory each month, before the $2\%$ addition.

(i) For $x=100$, show the end-March stock is $10299.9$ bushels to 1 d.p. [2]

(ii) Find the maximum monthly supply. [4]

A man enters a coma after an accident on 10 January 2013 and misses payment of his credit-card balance M dollars due on 27 January. On each monthly 27th, unpaid balances first receive $2\%$ interest and then an additional late fee L dollars.

(a) Express his balance on 1 February 2013 in terms of M and L. [1]

(b) Show that exactly n months after the accident, on the same day of the month, the accumulated balance is $(1.02)^nM+50L[(1.02)^n-1]$. [3]

(c) For $M=1000$, $L=55$, find the least n for which the balance first exceeds $2010. [2]