What is 5000[(1-(1+0.04)^{-4(3)})/(0.04)](1+0.04)^{-4(6)} ?

The solution to 5000[(1-(1+0.04)^{-4(3)})/(0.04)](1+0.04)^{-4(6)} is 18306.59406…

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simplify 5000[(1-(1+0.04)^{-4(3)})/(0.04)](1+0.04)^{-4(6)}

simplify

5000 [\frac{1 - ( 1 + 0.04 ) ^{- 4 (3)}}{0.04}] (1 + 0.04)^{- 4 (6)}

18306.59406 \dots

Solution steps

5000 [\frac{1 - ( 1 + 0.04 ) ^{- 4 (3)}}{0.04}] (1 + 0.04)^{- 4 (6)}

Apply exponent rule:

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

= 5000 \cdot \frac{1}{( 1 + 0.04 ) ^{4 \cdot 6}} [\frac{- ( 1 + 0.04 ) ^{- 4 \cdot 3} + 1}{0.04}]

Remove parentheses:

(a) = a

= 5000 \cdot \frac{1 - ( 1 + 0.04 ) ^{- 4 \cdot 3}}{0.04} \cdot \frac{1}{( 1 + 0.04 ) ^{4 \cdot 6}}

\frac{1 - ( 1 + 0.04 ) ^{- 4 \cdot 3}}{0.04} = \frac{0.37540 \dots}{0.04}

= 5000 \cdot \frac{1}{( 1 + 0.04 ) ^{4 \cdot 6}} \cdot \frac{0.37540 \dots}{0.04}

(1 + 0.04)^{4 \cdot 6} = 1.0 4^{24}

= 5000 \cdot \frac{1}{1.0 4 ^{24}} \cdot \frac{0.37540 \dots}{0.04}

Multiply fractions:

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

= \frac{0.37540 \dots \cdot 1 \cdot 5000}{0.04 \cdot 1.0 4 ^{24}}

Multiply the numbers:

0.37540 \dots \cdot 1 \cdot 5000 = 1877.01475 \dots

= \frac{1877.01475 \dots}{0.04 \cdot 1.0 4 ^{24}}

0.04 \cdot 1.0 4^{24} = 0.10253 \dots

= \frac{1877.01475 \dots}{0.10253 \dots}

Divide the numbers:

\frac{1877.01475 \dots}{0.10253 \dots} = 18306.59406 \dots

= 18306.59406 \dots

2 6^{2} 3

7500 (1 + \frac{0.015}{12})^{- 36}

(2)^{12}

What is 5000[(1-(1+0.04)^{-4(3)})/(0.04)](1+0.04)^{-4(6)} ?
The solution to 5000[(1-(1+0.04)^{-4(3)})/(0.04)](1+0.04)^{-4(6)} is 18306.59406…