Solve =-10,000+2000/(1+0.1)+4000/(1.01)^2+7000/(1.013^3)

$$= - 10,000 + \frac { 2000 } { ( 1 + 0.1 ) } + \frac { 4000 } { ( 1.01 ) ^ { 2 } } + \frac { 7000 } { ( 1.013 ^ { 3 } ) }$$

Evaluate

$$\frac{288498048006270000}{116644366504567}\approx 2473.313171065$$

Solution Steps

Add 1 and 0.1 to get 1.1.

$$-10000+\frac{2000}{1.1}+\frac{4000}{1.01^{2}}+\frac{7000}{1.013^{3}}$$

Expand \frac{2000}{1.1} by multiplying both numerator and the denominator by 10.

$$-10000+\frac{20000}{11}+\frac{4000}{1.01^{2}}+\frac{7000}{1.013^{3}}$$

Convert -10000 to fraction -\frac{110000}{11}.

$$-\frac{110000}{11}+\frac{20000}{11}+\frac{4000}{1.01^{2}}+\frac{7000}{1.013^{3}}$$

Since -\frac{110000}{11} and \frac{20000}{11} have the same denominator, add them by adding their numerators.

$$\frac{-110000+20000}{11}+\frac{4000}{1.01^{2}}+\frac{7000}{1.013^{3}}$$

Add -110000 and 20000 to get -90000.

$$-\frac{90000}{11}+\frac{4000}{1.01^{2}}+\frac{7000}{1.013^{3}}$$

Calculate 1.01 to the power of 2 and get 1.0201.

$$-\frac{90000}{11}+\frac{4000}{1.0201}+\frac{7000}{1.013^{3}}$$

Expand \frac{4000}{1.0201} by multiplying both numerator and the denominator by 10000.

$$-\frac{90000}{11}+\frac{40000000}{10201}+\frac{7000}{1.013^{3}}$$

Least common multiple of 11 and 10201 is 112211. Convert -\frac{90000}{11} and \frac{40000000}{10201} to fractions with denominator 112211.

$$-\frac{918090000}{112211}+\frac{440000000}{112211}+\frac{7000}{1.013^{3}}$$

Since -\frac{918090000}{112211} and \frac{440000000}{112211} have the same denominator, add them by adding their numerators.

$$\frac{-918090000+440000000}{112211}+\frac{7000}{1.013^{3}}$$

Add -918090000 and 440000000 to get -478090000.

$$-\frac{478090000}{112211}+\frac{7000}{1.013^{3}}$$

Calculate 1.013 to the power of 3 and get 1.039509197.

$$-\frac{478090000}{112211}+\frac{7000}{1.039509197}$$

Expand \frac{7000}{1.039509197} by multiplying both numerator and the denominator by 1000000000.

$$-\frac{478090000}{112211}+\frac{7000000000000}{1039509197}$$

Least common multiple of 112211 and 1039509197 is 116644366504567. Convert -\frac{478090000}{112211} and \frac{7000000000000}{1039509197} to fractions with denominator 116644366504567.

$$-\frac{496978951993730000}{116644366504567}+\frac{785477000000000000}{116644366504567}$$

Since -\frac{496978951993730000}{116644366504567} and \frac{785477000000000000}{116644366504567} have the same denominator, add them by adding their numerators.

$$\frac{-496978951993730000+785477000000000000}{116644366504567}$$

Add -496978951993730000 and 785477000000000000 to get 288498048006270000.

$$\frac{288498048006270000}{116644366504567}$$

Factor

$$\frac{3 \cdot 37 \cdot 19387 \cdot 13406311 \cdot 2 ^ {4} \cdot 5 ^ {4}}{11 \cdot 101 ^ {2} \cdot 1013 ^ {3}} = 2473\frac{36529640475825}{116644366504567} = 2473.313171064926$$