Needs

Hanka needs 40,000 € to buy an apartment. She can save or pay 300 € each month. The interest rate on deposits is 2%, the monthly deposit is 300 €, the state bonus is 8.5% of the deposit, and the interest rate on the loan is 2.9%. She will be in the savings phase for 3 years. What will be the possible loan amount? How many years will the construction loan be repaid?

Correct answer:

u =  26864.74 eur
n =  

Step-by-step explanation:

$$\begin{gathered} s=300\text{Eur} \\ q=1+\frac{2}{100}/12=\frac{601}{600}\doteq 1.0017 \\ p=1+\frac{8.5}{100}=\frac{217}{200}=1.085 \\ {m}_0=0 \\ {m}_1=m_0\cdot q+s=0\cdot 1.0017+300=300 \\ {m}_2=m_1\cdot q+s=300\cdot 1.0017+300=\frac{1201}{2}=600.5 \\ {m}_3=m_2\cdot q+s=600.5\cdot 1.0017+300\doteq 901.5008 \\ {m}_4=m_3\cdot q+s=901.5008\cdot 1.0017+300\doteq 1203.0033 \\ {m}_5=m_4\cdot q+s=1203.0033\cdot 1.0017+300\doteq 1505.0083 \\ {m}_6=m_5\cdot q+s=1505.0083\cdot 1.0017+300\doteq 1807.5167 \\ {m}_7=m_6\cdot q+s=1807.5167\cdot 1.0017+300\doteq 2110.5292 \\ {m}_8=m_7\cdot q+s=2110.5292\cdot 1.0017+300\doteq 2414.0468 \\ {m}_9=m_8\cdot q+s=2414.0468\cdot 1.0017+300\doteq 2718.0702 \\ {m}_{10}=m_9\cdot q+s=2718.0702\cdot 1.0017+300\doteq 3022.6003 \\ {m}_{11}=m_{10}\cdot q+s=3022.6003\cdot 1.0017+300\doteq 3327.638 \\ {m}_{12}=(m_{11}\cdot q+s)\cdot p=(3327.638\cdot 1.0017+300)\cdot 1.085\doteq 3942.0047 \\ {m}_{13}=m_{12}\cdot q+s=3942.0047\cdot 1.0017+300\doteq 4248.5747 \\ {m}_{14}=m_{13}\cdot q+s=4248.5747\cdot 1.0017+300\doteq 4555.6556 \\ {m}_{15}=m_{14}\cdot q+s=4555.6556\cdot 1.0017+300\doteq 4863.2484 \\ {m}_{16}=m_{15}\cdot q+s=4863.2484\cdot 1.0017+300\doteq 5171.3538 \\ {m}_{17}=m_{16}\cdot q+s=5171.3538\cdot 1.0017+300\doteq 5479.9727 \\ {m}_{18}=m_{17}\cdot q+s=5479.9727\cdot 1.0017+300\doteq 5789.106 \\ {m}_{19}=m_{18}\cdot q+s=5789.106\cdot 1.0017+300\doteq 6098.7545 \\ {m}_{20}=m_{19}\cdot q+s=6098.7545\cdot 1.0017+300\doteq 6408.9191 \\ {m}_{21}=m_{20}\cdot q+s=6408.9191\cdot 1.0017+300\doteq 6719.6006 \\ {m}_{22}=m_{21}\cdot q+s=6719.6006\cdot 1.0017+300\doteq 7030.8 \\ {m}_{23}=m_{22}\cdot q+s=7030.8\cdot 1.0017+300\doteq 7342.518 \\ {m}_{24}=(m_{23}\cdot q+s)\cdot p=(7342.518\cdot 1.0017+300)\cdot 1.085\doteq 8305.4097 \\ {m}_{25}=m_{24}\cdot q+s=8305.4097\cdot 1.0017+300\doteq 8619.2521 \\ {m}_{26}=m_{25}\cdot q+s=8619.2521\cdot 1.0017+300\doteq 8933.6175 \\ {m}_{27}=m_{26}\cdot q+s=8933.6175\cdot 1.0017+300\doteq 9248.5069 \\ {m}_{28}=m_{27}\cdot q+s=9248.5069\cdot 1.0017+300\doteq 9563.921 \\ {m}_{29}=m_{28}\cdot q+s=9563.921\cdot 1.0017+300\doteq 9879.8609 \\ {m}_{30}=m_{29}\cdot q+s=9879.8609\cdot 1.0017+300\doteq 10196.3273 \\ {m}_{31}=m_{30}\cdot q+s=10196.3273\cdot 1.0017+300\doteq 10513.3212 \\ {m}_{32}=m_{31}\cdot q+s=10513.3212\cdot 1.0017+300\doteq 10830.8434 \\ {m}_{33}=m_{32}\cdot q+s=10830.8434\cdot 1.0017+300\doteq 11148.8948 \\ {m}_{34}=m_{33}\cdot q+s=11148.8948\cdot 1.0017+300\doteq 11467.4763 \\ {m}_{35}=m_{34}\cdot q+s=11467.4763\cdot 1.0017+300\doteq 11786.5888 \\ {m}_{36}=(m_{35}\cdot q+s)\cdot p=(11786.5888\cdot 1.0017+300)\cdot 1.085\doteq 13135.2629 \\ u=[40000-m_{36},2]=[40000-13135.2629,2]=26864.74\text{eur} \end{gathered}$$

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