Slow saving in banks

How long will it take to save € 9,000 by depositing € 200 at the beginning of each year at 2% interest?

Correct result:

y = 32

Solution:

q = 2 % = 1 + \frac{2}{100} = 1.02 v = 200 eur r_{1} = v \cdot q = 200 \cdot 1.02 = 204 eur r_{2} = (r_{1} + v) \cdot q = (204 + 200) \cdot 1.02 = \frac{10302}{25} = 412.08 r_{3} = (r_{2} + v) \cdot q = (412.08 + 200) \cdot 1.02 = 624.3216 r_{4} = (r_{3} + v) \cdot q = (624.3216 + 200) \cdot 1.02 ≐ 840.808 r_{5} = (r_{4} + v) \cdot q = (840.808 + 200) \cdot 1.02 ≐ 1061.6242 r_{6} = (r_{5} + v) \cdot q = (1061.6242 + 200) \cdot 1.02 ≐ 1286.8567 r_{7} = (r_{6} + v) \cdot q = (1286.8567 + 200) \cdot 1.02 ≐ 1516.5938 r_{8} = (r_{7} + v) \cdot q = (1516.5938 + 200) \cdot 1.02 ≐ 1750.9257 r_{9} = (r_{8} + v) \cdot q = (1750.9257 + 200) \cdot 1.02 = 1989.9442 r_{10} = (r_{9} + v) \cdot q = (1989.9442 + 200) \cdot 1.02 ≐ 2233.7431 r_{11} = (r_{10} + v) \cdot q = (2233.7431 + 200) \cdot 1.02 ≐ 2482.4179 r_{12} = (r_{11} + v) \cdot q = (2482.4179 + 200) \cdot 1.02 ≐ 2736.0663 r_{13} = (r_{12} + v) \cdot q = (2736.0663 + 200) \cdot 1.02 ≐ 2994.7876 r_{14} = (r_{13} + v) \cdot q = (2994.7876 + 200) \cdot 1.02 ≐ 3258.6834 r_{15} = (r_{14} + v) \cdot q = (3258.6834 + 200) \cdot 1.02 ≐ 3527.8571 r_{16} = (r_{15} + v) \cdot q = (3527.8571 + 200) \cdot 1.02 ≐ 3802.4142 r_{17} = (r_{16} + v) \cdot q = (3802.4142 + 200) \cdot 1.02 ≐ 4082.4625 r_{18} = (r_{17} + v) \cdot q = (4082.4625 + 200) \cdot 1.02 ≐ 4368.1117 r_{19} = (r_{18} + v) \cdot q = (4368.1117 + 200) \cdot 1.02 ≐ 4659.474 r_{20} = (r_{19} + v) \cdot q = (4659.474 + 200) \cdot 1.02 ≐ 4956.6634 r_{21} = (r_{20} + v) \cdot q = (4956.6634 + 200) \cdot 1.02 ≐ 5259.7967 r_{22} = (r_{21} + v) \cdot q = (5259.7967 + 200) \cdot 1.02 ≐ 5568.9926 r_{23} = (r_{22} + v) \cdot q = (5568.9926 + 200) \cdot 1.02 ≐ 5884.3725 r_{24} = (r_{23} + v) \cdot q = (5884.3725 + 200) \cdot 1.02 ≐ 6206.0599 r_{25} = (r_{24} + v) \cdot q = (6206.0599 + 200) \cdot 1.02 ≐ 6534.1811 r_{26} = (r_{25} + v) \cdot q = (6534.1811 + 200) \cdot 1.02 ≐ 6868.8648 r_{27} = (r_{26} + v) \cdot q = (6868.8648 + 200) \cdot 1.02 ≐ 7210.2421 r_{28} = (r_{27} + v) \cdot q = (7210.2421 + 200) \cdot 1.02 ≐ 7558.4469 r_{29} = (r_{28} + v) \cdot q = (7558.4469 + 200) \cdot 1.02 ≐ 7913.6158 r_{30} = (r_{29} + v) \cdot q = (7913.6158 + 200) \cdot 1.02 ≐ 8275.8882 r_{31} = (r_{30} + v) \cdot q = (8275.8882 + 200) \cdot 1.02 ≐ 8645.4059 r_{32} = (r_{31} + v) \cdot q = (8645.4059 + 200) \cdot 1.02 ≐ 9022.314 r_{33} = (r_{32} + v) \cdot q = (9022.314 + 200) \cdot 1.02 ≐ 9406.7603 r_{34} = (r_{33} + v) \cdot q = (9406.7603 + 200) \cdot 1.02 ≐ 9798.8955 r_{35} = (r_{34} + v) \cdot q = (9798.8955 + 200) \cdot 1.02 ≐ 10198.8734 y = 32

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