Saving for an apartment

The Adamec, Benda and Cibulka families began saving for an apartment priced at 750 000 Kč in January 1997. The Benda family had 250 000 and save 4 000 Kč monthly; the Adamec family had 370 000 Kč (Kč is Czech crown) and save 6 000 Kč monthly; the Cibulka family had 186 000 and save 10 000 Kč monthly.

A) find out in which month of which year each of the mentioned families will have saved for the apartment.
B) what amount would the mentioned families have to save monthly in order to buy the apartment in three years?

Final Answer:

a₁ =  125 m
b₁ =  64 m
c₁ =  57 m
a₂ =  13888.8889 Kc
b₂ =  10555.5556 Kc
c₂ =  15666.6667 Kc

Step-by-step explanation:

$$\begin{gathered} b=750000 \\ {a}_1=(b-250000)/4000=(750000-250000)/4000=125\text{m} \end{gathered}$$

$$\begin{gathered} b_{11}=(b-370000)/6000=(750000-370000)/6000=\frac{190}{3}\doteq 63.3333 \\ {b}_1=\lceil b_{11}\rceil =\lceil 63.3333\rceil =64\text{m} \end{gathered}$$

$$\begin{gathered} c_{11}=(b-186000)/10000=(750000-186000)/10000=\frac{282}{5}=56.4 \\ {c}_1=\lceil c_{11}\rceil =\lceil 56.4\rceil =57\text{m} \end{gathered}$$

$a_2=(b-250000)/(3\cdot 12)=(750000-250000)/(3\cdot 12)=13888.8889\text{Kc}$

$b_2=(b-370000)/(3\cdot 12)=(750000-370000)/(3\cdot 12)=10555.5556\text{Kc}$

$c_2=(b-186000)/(3\cdot 12)=(750000-186000)/(3\cdot 12)=15666.6667\text{Kc}$

Try another example