簡約 5000([1-(1.04)^{-9}])/(0.04)(1.04)^{-3}

解

簡約

5000 \frac{[ 1 - ( 1.04 ) ^{- 9} ]}{0.04} (1.04)^{- 3}

33049.91363 \dots

解答ステップ

5000 \cdot \frac{[ 1 - ( 1.04 ) ^{- 9} ]}{0.04} (1.04)^{- 3}

指数の規則を適用する:

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

= 5000 \cdot \frac{1}{1.0 4 ^{3}} \cdot \frac{[ 1 - 1.0 4 ^{- 9} ]}{0.04}

\frac{1 - 1.0 4 ^{- 9}}{0.04} = \frac{0.29741 \dots}{0.04}

= 5000 \cdot \frac{1}{1.0 4 ^{3}} \cdot \frac{0.29741 \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{0.29741 \dots \cdot 1 \cdot 5000}{0.04 \cdot 1.0 4 ^{3}}

数を乗じる:

0.29741 \dots \cdot 1 \cdot 5000 = 1487.06632 \dots

= \frac{1487.06632 \dots}{0.04 \cdot 1.0 4 ^{3}}

0.04 \cdot 1.0 4^{3} = 0.04499456

= \frac{1487.06632 \dots}{0.04499456}

数を割る:

\frac{1487.06632 \dots}{0.04499456} = 33049.91363 \dots

= 33049.91363 \dots