Solve -100,000+40,000/(1+.25)+40,000/(1+.25)^2+(1+.25)^3+(1+.25)^4+(1+.25)^5=1

$$- 100,000 + \frac { 40,000 } { ( 1 + .25 ) } + \frac { 40,000 } { ( 1 + .25 ) ^ { 2 } } + ( 1 + .25 ) ^ { 3 } + ( 1 + .25 ) ^ { 4 } + ( 1 + .25 ) ^ { 5 } = 1$$

Verify

Solution Steps

Add 1 and 0.25 to get 1.25.

$$-100000+\frac{40000}{1.25}+\frac{40000}{\left(1+0.25\right)^{2}}+\left(1+0.25\right)^{3}+\left(1+0.25\right)^{4}+\left(1+0.25\right)^{5}=1$$

Expand \frac{40000}{1.25} by multiplying both numerator and the denominator by 100.

$$-100000+\frac{4000000}{125}+\frac{40000}{\left(1+0.25\right)^{2}}+\left(1+0.25\right)^{3}+\left(1+0.25\right)^{4}+\left(1+0.25\right)^{5}=1$$

Divide 4000000 by 125 to get 32000.

$$-100000+32000+\frac{40000}{\left(1+0.25\right)^{2}}+\left(1+0.25\right)^{3}+\left(1+0.25\right)^{4}+\left(1+0.25\right)^{5}=1$$

Add -100000 and 32000 to get -68000.

$$-68000+\frac{40000}{\left(1+0.25\right)^{2}}+\left(1+0.25\right)^{3}+\left(1+0.25\right)^{4}+\left(1+0.25\right)^{5}=1$$

Add 1 and 0.25 to get 1.25.

$$-68000+\frac{40000}{1.25^{2}}+\left(1+0.25\right)^{3}+\left(1+0.25\right)^{4}+\left(1+0.25\right)^{5}=1$$

Calculate 1.25 to the power of 2 and get 1.5625.

$$-68000+\frac{40000}{1.5625}+\left(1+0.25\right)^{3}+\left(1+0.25\right)^{4}+\left(1+0.25\right)^{5}=1$$

Expand \frac{40000}{1.5625} by multiplying both numerator and the denominator by 10000.

$$-68000+\frac{400000000}{15625}+\left(1+0.25\right)^{3}+\left(1+0.25\right)^{4}+\left(1+0.25\right)^{5}=1$$

Divide 400000000 by 15625 to get 25600.

$$-68000+25600+\left(1+0.25\right)^{3}+\left(1+0.25\right)^{4}+\left(1+0.25\right)^{5}=1$$

Add -68000 and 25600 to get -42400.

$$-42400+\left(1+0.25\right)^{3}+\left(1+0.25\right)^{4}+\left(1+0.25\right)^{5}=1$$

Add 1 and 0.25 to get 1.25.

$$-42400+1.25^{3}+\left(1+0.25\right)^{4}+\left(1+0.25\right)^{5}=1$$

Calculate 1.25 to the power of 3 and get 1.953125.

$$-42400+1.953125+\left(1+0.25\right)^{4}+\left(1+0.25\right)^{5}=1$$

Add -42400 and 1.953125 to get -42398.046875.

$$-42398.046875+\left(1+0.25\right)^{4}+\left(1+0.25\right)^{5}=1$$

Add 1 and 0.25 to get 1.25.

$$-42398.046875+1.25^{4}+\left(1+0.25\right)^{5}=1$$

Calculate 1.25 to the power of 4 and get 2.44140625.

$$-42398.046875+2.44140625+\left(1+0.25\right)^{5}=1$$

Add -42398.046875 and 2.44140625 to get -42395.60546875.

$$-42395.60546875+\left(1+0.25\right)^{5}=1$$

Add 1 and 0.25 to get 1.25.

$$-42395.60546875+1.25^{5}=1$$

Calculate 1.25 to the power of 5 and get 3.0517578125.

$$-42395.60546875+3.0517578125=1$$

Add -42395.60546875 and 3.0517578125 to get -42392.5537109375.

$$-42392.5537109375=1$$

Compare -42392.5537109375 and 1.

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