Annual pension

Calculate the amount of money that must be deposited into a bank account with an annual interest rate of 2% in order to generate annual pension payments of €1,000, payable at the end of each year for 10 years.

Final Answer:

x =  8998.99 Eur

Step-by-step explanation:

$$\begin{gathered} q=1.02 \\ {x}_1 \\ {x}_2=q{x}_1-1000 \\ {x}_3=q{x}_2-1000 \\ \dots . \\ {x}_{10}=q{x}_9-1000 \\ {x}_{10}=1000 \\ {x}_9=(x_{10}+1000)/q=(1000+1000)/1.02\doteq 1960.7843\text{Eur} \\ {x}_8=(x_9+1000)/q=(1960.7843+1000)/1.02\doteq 2902.7297\text{Eur} \\ {x}_7=(x_8+1000)/q=(2902.7297+1000)/1.02\doteq 3826.2056\text{Eur} \\ {x}_6=(x_7+1000)/q=(3826.2056+1000)/1.02\doteq 4731.5741\text{Eur} \\ {x}_5=(x_6+1000)/q=(4731.5741+1000)/1.02\doteq 5619.1903\text{Eur} \\ {x}_4=(x_5+1000)/q=(5619.1903+1000)/1.02\doteq 6489.4023\text{Eur} \\ {x}_3=(x_4+1000)/q=(6489.4023+1000)/1.02\doteq 7342.5512\text{Eur} \\ {x}_2=(x_3+1000)/q=(7342.5512+1000)/1.02\doteq 8178.9718\text{Eur} \\ {x}_1=(x_2+1000)/q=(8178.9718+1000)/1.02\doteq 8998.992\text{Eur} \\ x=x_1=8998.992=8998.99\text{Eur} \end{gathered}$$

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