Annual pension

Calculate the amount of money generating an annual pension of EUR 1000, payable at the end of the year and for a period of 10 years, shall be inserted into the bank to account with an annual interest rate of 2%

Correct result:

x =  8998.99 Eur

Solution:

q=1.02  x1 x2=qx1−1000 x3=qx2−1000 …. x10=qx9−1000  x10=1000  x9=(x10+1000)/q=(1000+1000)/1.02≐1960.7843 Eur x8=(x9+1000)/q=(1960.7843+1000)/1.02≐2902.7297 Eur x7=(x8+1000)/q=(2902.7297+1000)/1.02≐3826.2056 Eur x6=(x7+1000)/q=(3826.2056+1000)/1.02≐4731.5741 Eur x5=(x6+1000)/q=(4731.5741+1000)/1.02≐5619.1903 Eur x4=(x5+1000)/q=(5619.1903+1000)/1.02≐6489.4023 Eur x3=(x4+1000)/q=(6489.4023+1000)/1.02≐7342.5512 Eur x2=(x3+1000)/q=(7342.5512+1000)/1.02≐8178.9718 Eur x1=(x2+1000)/q=(8178.9718+1000)/1.02≐8998.992 Eur  x=x1=8998.992=8998.99 Eur=9.0⋅103 Eur

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