Solve 20,000(0.07/12)/1-(1+frac{0.07{12})^-12(3)}

$$\frac { 20,000 ( \frac { 0.07 } { 12 } ) } { 1 - ( 1 + \frac { 0.07 } { 12 } ) ^ { - 12 ( 3 ) } }$$

Evaluate

$$\frac{43694998406037084299810227910543317447982632863504270673778384615687496228938935854511965268724225622205845960050}{70756325629564217406368679086270223318708281687179462918100439563035681962333735895816845160493362476050108229}\approx 617.541937307$$

Solution Steps

Expand \frac{0.07}{12} by multiplying both numerator and the denominator by 100.

$$\frac{20000\times \frac{7}{1200}}{1-\left(1+\frac{0.07}{12}\right)^{-12\times 3}}$$

Multiply 20000 and \frac{7}{1200} to get \frac{350}{3}.

$$\frac{\frac{350}{3}}{1-\left(1+\frac{0.07}{12}\right)^{-12\times 3}}$$

Expand \frac{0.07}{12} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{350}{3}}{1-\left(1+\frac{7}{1200}\right)^{-12\times 3}}$$

Add 1 and \frac{7}{1200} to get \frac{1207}{1200}.

$$\frac{\frac{350}{3}}{1-\left(\frac{1207}{1200}\right)^{-12\times 3}}$$

Multiply -12 and 3 to get -36.

$$\frac{\frac{350}{3}}{1-\left(\frac{1207}{1200}\right)^{-36}}$$

Calculate \frac{1207}{1200} to the power of -36 and get \frac{708801874985091845381344307009569161216000000000000000000000000000000000000000000000000000000000000000000000000}{873899968120741685996204558210866348959652657270085413475567692313749924578778717090239305374484512444116919201}.

$$\frac{\frac{350}{3}}{1-\frac{708801874985091845381344307009569161216000000000000000000000000000000000000000000000000000000000000000000000000}{873899968120741685996204558210866348959652657270085413475567692313749924578778717090239305374484512444116919201}}$$

Subtract \frac{708801874985091845381344307009569161216000000000000000000000000000000000000000000000000000000000000000000000000}{873899968120741685996204558210866348959652657270085413475567692313749924578778717090239305374484512444116919201} from 1 to get \frac{165098093135649840614860251201297187743652657270085413475567692313749924578778717090239305374484512444116919201}{873899968120741685996204558210866348959652657270085413475567692313749924578778717090239305374484512444116919201}.

$$\frac{\frac{350}{3}}{\frac{165098093135649840614860251201297187743652657270085413475567692313749924578778717090239305374484512444116919201}{873899968120741685996204558210866348959652657270085413475567692313749924578778717090239305374484512444116919201}}$$

Divide \frac{350}{3} by \frac{165098093135649840614860251201297187743652657270085413475567692313749924578778717090239305374484512444116919201}{873899968120741685996204558210866348959652657270085413475567692313749924578778717090239305374484512444116919201} by multiplying \frac{350}{3} by the reciprocal of \frac{165098093135649840614860251201297187743652657270085413475567692313749924578778717090239305374484512444116919201}{873899968120741685996204558210866348959652657270085413475567692313749924578778717090239305374484512444116919201}.

$$\frac{350}{3}\times \frac{873899968120741685996204558210866348959652657270085413475567692313749924578778717090239305374484512444116919201}{165098093135649840614860251201297187743652657270085413475567692313749924578778717090239305374484512444116919201}$$

Multiply \frac{350}{3} and \frac{873899968120741685996204558210866348959652657270085413475567692313749924578778717090239305374484512444116919201}{165098093135649840614860251201297187743652657270085413475567692313749924578778717090239305374484512444116919201} to get \frac{43694998406037084299810227910543317447982632863504270673778384615687496228938935854511965268724225622205845960050}{70756325629564217406368679086270223318708281687179462918100439563035681962333735895816845160493362476050108229}.

$$\frac{43694998406037084299810227910543317447982632863504270673778384615687496228938935854511965268724225622205845960050}{70756325629564217406368679086270223318708281687179462918100439563035681962333735895816845160493362476050108229}$$