簡約 250(1.04)^{-4}((1-(1.04)^{-10})/(0.04))

解

簡約

250 (1.04)^{- 4} (\frac{1 - ( 1.04 ) ^{- 10}}{0.04})

1733.30692 \dots

解答ステップ

250 (1.04)^{- 4} (\frac{1 - ( 1.04 ) ^{- 10}}{0.04})

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

= 250 \cdot \frac{1}{1.0 4 ^{4}} \cdot \frac{1 - 1.0 4 ^{- 10}}{0.04}

\frac{1 - 1.0 4 ^{- 10}}{0.04} = \frac{0.32443 \dots}{0.04}

= 250 \cdot \frac{1}{1.0 4 ^{4}} \cdot \frac{0.32443 \dots}{0.04}

分数を乗じる:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{1 \cdot 0.32443 \dots \cdot 250}{1.0 4 ^{4} \cdot 0.04}

数を乗じる:

1 \cdot 0.32443 \dots \cdot 250 = 81.10895 \dots

= \frac{81.10895 \dots}{0.04 \cdot 1.0 4 ^{4}}

1.0 4^{4} \cdot 0.04 = 0.0467943424

= \frac{81.10895 \dots}{0.0467943424}

数を割る:

\frac{81.10895 \dots}{0.0467943424} = 1733.30692 \dots

= 1733.30692 \dots