Inspector and fare-dodging

Jirka rode as a fare-dodger and was caught by the inspector. He was supposed to pay 1 500 Kč, but at first he did not have money and then he forgot about it. If he does not pay on time, for each day of delay he will be charged a penalty amounting to 0.5‰ of the owed amount.

a) By how much will his debt grow if he only remembers about it three months after the expiry of the deadline?
b) By how much will his debt grow if the collection agency, to which the transport company re-sold the receivable, contacts him after two years?

(The statement of the example does not describe the reality exactly. Already on the second day of delay, the debtor in fact owes a greater amount than 1 500 Kč - he owes the original owed amount 1 500 Kč + penalty from delay for the previous day. The penalty which he should pay for the second day is thus imperceptibly greater than the penalty for the previous day. If he further does not pay, every further day the amount he owes grows, and so does the amount he pays as penalty. The solution of this situation using geometric series is not difficult, but is so far beyond our possibilities.)

Final Answer:

a =  1569.0241
b =  2160.5739 Kc

Step-by-step explanation:

$$\begin{gathered} p=1500\text{Kc} \\ q=0.5‰=\frac{0.5}{1000}=0.0005 \\ {d}_1=3\cdot 30=90 \\ a=p\cdot (1+q{)}^{d_1}=1500\cdot (1+0.0005{)}^{90}=1569.0241 \end{gathered}$$

$$\begin{gathered} d_2=2\cdot 365=730 \\ b=p\cdot (1+q{)}^{d_2}=1500\cdot (1+0.0005{)}^{730}=2160.5739\text{Kc} \end{gathered}$$

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