Solve 43000.145/12/1-{left(1+frac{0.145{12}right)}^-12*4}

$$\frac{ 4300 \frac{ 0.145 }{ 12 } }{ 1- { \left(1+ \frac{ 0.145 }{ 12 } \right) }^{ -12 \cdot 4 } }$$

Evaluate

$$\frac{32673949113275931467475103642148099915583061511611243402926145772539328692030752110989489244777030568285566045255044873712040106261151872425327665890952397587727889938269}{3329328770585028461953199522197195686942287891524030079658209859063024320113228854916471086221257068549454513026281970419743612641666461772615793825607055388172546400}\approx 9813.974937517$$

Solution Steps

Multiply 4300 and 12 to get 51600.

$$\frac{\frac{51600+0.145}{12}}{1-\left(1+\frac{0.145}{12}\right)^{-12\times 4}}$$

Add 51600 and 0.145 to get 51600.145.

$$\frac{\frac{51600.145}{12}}{1-\left(1+\frac{0.145}{12}\right)^{-12\times 4}}$$

Expand \frac{51600.145}{12} by multiplying both numerator and the denominator by 1000.

$$\frac{\frac{51600145}{12000}}{1-\left(1+\frac{0.145}{12}\right)^{-12\times 4}}$$

Reduce the fraction \frac{51600145}{12000} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{10320029}{2400}}{1-\left(1+\frac{0.145}{12}\right)^{-12\times 4}}$$

Expand \frac{0.145}{12} by multiplying both numerator and the denominator by 1000.

$$\frac{\frac{10320029}{2400}}{1-\left(1+\frac{145}{12000}\right)^{-12\times 4}}$$

Reduce the fraction \frac{145}{12000} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{10320029}{2400}}{1-\left(1+\frac{29}{2400}\right)^{-12\times 4}}$$

Add 1 and \frac{29}{2400} to get \frac{2429}{2400}.

$$\frac{\frac{10320029}{2400}}{1-\left(\frac{2429}{2400}\right)^{-12\times 4}}$$

Multiply -12 and 4 to get -48.

$$\frac{\frac{10320029}{2400}}{1-\left(\frac{2429}{2400}\right)^{-48}}$$

Calculate \frac{2429}{2400} to the power of -48 and get \frac{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{3166071443527526082288635394546672292837845854077662320806089379452260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561}.

$$\frac{\frac{10320029}{2400}}{1-\frac{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{3166071443527526082288635394546672292837845854077662320806089379452260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561}}$$

Subtract \frac{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{3166071443527526082288635394546672292837845854077662320806089379452260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561} from 1 to get \frac{1387220321077095192480499800915498202892619954801679199857587441276260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561}{3166071443527526082288635394546672292837845854077662320806089379452260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561}.

$$\frac{\frac{10320029}{2400}}{\frac{1387220321077095192480499800915498202892619954801679199857587441276260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561}{3166071443527526082288635394546672292837845854077662320806089379452260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561}}$$

Divide \frac{10320029}{2400} by \frac{1387220321077095192480499800915498202892619954801679199857587441276260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561}{3166071443527526082288635394546672292837845854077662320806089379452260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561} by multiplying \frac{10320029}{2400} by the reciprocal of \frac{1387220321077095192480499800915498202892619954801679199857587441276260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561}{3166071443527526082288635394546672292837845854077662320806089379452260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561}.

$$\frac{10320029}{2400}\times \frac{3166071443527526082288635394546672292837845854077662320806089379452260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561}{1387220321077095192480499800915498202892619954801679199857587441276260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561}$$

Multiply \frac{10320029}{2400} and \frac{3166071443527526082288635394546672292837845854077662320806089379452260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561}{1387220321077095192480499800915498202892619954801679199857587441276260133380512022881862952592190445228939380427617487674893171934027692405256580760669606411738561} to get \frac{32673949113275931467475103642148099915583061511611243402926145772539328692030752110989489244777030568285566045255044873712040106261151872425327665890952397587727889938269}{3329328770585028461953199522197195686942287891524030079658209859063024320113228854916471086221257068549454513026281970419743612641666461772615793825607055388172546400}.

$$\frac{32673949113275931467475103642148099915583061511611243402926145772539328692030752110989489244777030568285566045255044873712040106261151872425327665890952397587727889938269}{3329328770585028461953199522197195686942287891524030079658209859063024320113228854916471086221257068549454513026281970419743612641666461772615793825607055388172546400}$$