Solve 11001.0225^12-1/0.0225+9609.721.0225^12

$$1100 \frac{ { 1.0225 }^{ 12 } -1 }{ 0.0225 } +9609.72 { 1.0225 }^{ 12 }$$

Evaluate

$$27513.218658881249518889364231600338180065155029296875$$

Solution Steps

Calculate 1.0225 to the power of 12 and get 1.306049989887568163387293232660353183746337890625.

$$1100\times \frac{1.306049989887568163387293232660353183746337890625-1}{0.0225}+9609.72\times 1.0225^{12}$$

Subtract 1 from 1.306049989887568163387293232660353183746337890625 to get 0.306049989887568163387293232660353183746337890625.

$$1100\times \frac{0.306049989887568163387293232660353183746337890625}{0.0225}+9609.72\times 1.0225^{12}$$

Expand \frac{0.306049989887568163387293232660353183746337890625}{0.0225} by multiplying both numerator and the denominator by 1000000000000000000000000000000000000000000000000.

$$1100\times \frac{306049989887568163387293232660353183746337890625}{22500000000000000000000000000000000000000000000}+9609.72\times 1.0225^{12}$$

Reduce the fraction \frac{306049989887568163387293232660353183746337890625}{22500000000000000000000000000000000000000000000} to lowest terms by extracting and canceling out 536441802978515625.

$$1100\times \frac{570518531904616310207990024409}{41943040000000000000000000000}+9609.72\times 1.0225^{12}$$

Express 1100\times \frac{570518531904616310207990024409}{41943040000000000000000000000} as a single fraction.

$$\frac{1100\times 570518531904616310207990024409}{41943040000000000000000000000}+9609.72\times 1.0225^{12}$$

Multiply 1100 and 570518531904616310207990024409 to get 627570385095077941228789026849900.

$$\frac{627570385095077941228789026849900}{41943040000000000000000000000}+9609.72\times 1.0225^{12}$$

Reduce the fraction \frac{627570385095077941228789026849900}{41943040000000000000000000000} to lowest terms by extracting and canceling out 100.

$$\frac{6275703850950779412287890268499}{419430400000000000000000000}+9609.72\times 1.0225^{12}$$

Calculate 1.0225 to the power of 12 and get 1.306049989887568163387293232660353183746337890625.

$$\frac{6275703850950779412287890268499}{419430400000000000000000000}+9609.72\times 1.306049989887568163387293232660353183746337890625$$

Multiply 9609.72 and 1.306049989887568163387293232660353183746337890625 to get 12550.774708822361531066139523760849196910858154296875.

$$\frac{6275703850950779412287890268499}{419430400000000000000000000}+12550.774708822361531066139523760849196910858154296875$$

Convert decimal number 12550.774708822361531066139523760849196910858154296875 to fraction \frac{5264176456431246625919683326906822483}{10000000000}. Reduce the fraction \frac{5264176456431246625919683326906822483}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{6275703850950779412287890268499}{419430400000000000000000000}+\frac{5264176456431246625919683326906822483}{419430400000000000000000000000000}$$

Least common multiple of 419430400000000000000000000 and 419430400000000000000000000000000 is 419430400000000000000000000000000. Convert \frac{6275703850950779412287890268499}{419430400000000000000000000} and \frac{5264176456431246625919683326906822483}{419430400000000000000000000000000} to fractions with denominator 419430400000000000000000000000000.

$$\frac{6275703850950779412287890268499000000}{419430400000000000000000000000000}+\frac{5264176456431246625919683326906822483}{419430400000000000000000000000000}$$

Since \frac{6275703850950779412287890268499000000}{419430400000000000000000000000000} and \frac{5264176456431246625919683326906822483}{419430400000000000000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{6275703850950779412287890268499000000+5264176456431246625919683326906822483}{419430400000000000000000000000000}$$

Add 6275703850950779412287890268499000000 and 5264176456431246625919683326906822483 to get 11539880307382026038207573595405822483.

$$\frac{11539880307382026038207573595405822483}{419430400000000000000000000000000}$$

Factor

$$\frac{3 \cdot 31 \cdot 1013 \cdot 122492334144105404347860327520787}{2 ^ {48} \cdot 5 ^ {26}} = 27513\frac{9.171218202685202 \times 10^{31}}{4.194304 \times 10^{32}} = 27513.21865888125$$