What is 500[((1+0.03)^{24}-1)/(0.03(1+0.03)^{24)}](1+0.03)^{-6} ?

The solution to 500[((1+0.03)^{24}-1)/(0.03(1+0.03)^{24)}](1+0.03)^{-6} is 7091.62495…

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simplify 500[((1+0.03)^{24}-1)/(0.03(1+0.03)^{24)}](1+0.03)^{-6}

simplify

500 [\frac{( 1 + 0.03 ) ^{24} - 1}{0.03 ( 1 + 0.03 ) ^{24}}] (1 + 0.03)^{- 6}

7091.62495 \dots

Solution steps

500 [\frac{( 1 + 0.03 ) ^{24} - 1}{0.03 ( 1 + 0.03 ) ^{24}}] (1 + 0.03)^{- 6}

Apply exponent rule:

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

= 500 \cdot \frac{1}{( 1 + 0.03 ) ^{6}} [\frac{( 1 + 0.03 ) ^{24} - 1}{0.03 ( 1 + 0.03 ) ^{24}}]

Remove parentheses:

(a) = a

= 500 \cdot \frac{( 1 + 0.03 ) ^{24} - 1}{0.03 ( 1 + 0.03 ) ^{24}} \cdot \frac{1}{( 1 + 0.03 ) ^{6}}

\frac{( 1 + 0.03 ) ^{24} - 1}{0.03 ( 1 + 0.03 ) ^{24}} = \frac{1.03279 \dots}{0.03 \cdot 1.0 3 ^{24}}

= 500 \cdot \frac{1}{( 1 + 0.03 ) ^{6}} \cdot \frac{1.03279 \dots}{0.03 \cdot 1.0 3 ^{24}}

Add the numbers:

1 + 0.03 = 1.03

= 500 \cdot \frac{1}{1.0 3 ^{6}} \cdot \frac{1.03279 \dots}{0.03 \cdot 1.0 3 ^{24}}

Multiply fractions:

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

= \frac{1.03279 \dots \cdot 1 \cdot 500}{0.03 \cdot 1.0 3 ^{24} \cdot 1.0 3 ^{6}}

Multiply the numbers:

1.03279 \dots \cdot 1 \cdot 500 = 516.39705 \dots

= \frac{516.39705 \dots}{0.03 \cdot 1.0 3 ^{24} \cdot 1.0 3 ^{6}}

0.03 \cdot 1.0 3^{24} \cdot 1.0 3^{6} = 0.03 \cdot 1.0 3^{30}

= \frac{516.39705 \dots}{0.03 \cdot 1.0 3 ^{30}}

0.03 \cdot 1.0 3^{30} = 0.07281 \dots

= \frac{516.39705 \dots}{0.07281 \dots}

Divide the numbers:

\frac{516.39705 \dots}{0.07281 \dots} = 7091.62495 \dots

= 7091.62495 \dots

4.1 \cdot 1 0^{- 8}

e^{- t^{2}} \cdot e^{t^{2}}

4.1 \cdot 1 0^{- 6}

(- x + 6)^{2} (- x - 2)^{2}

What is 500[((1+0.03)^{24}-1)/(0.03(1+0.03)^{24)}](1+0.03)^{-6} ?
The solution to 500[((1+0.03)^{24}-1)/(0.03(1+0.03)^{24)}](1+0.03)^{-6} is 7091.62495…