Solve 100/1.06^20+4*(1-1/1.06^20)1/0.06=

$$\frac{ 100 }{ { 1.06 }^{ 20 } } +4 \times (1- \frac{ 1 }{ { 1.06 }^{ 20 } } ) \frac{ 1 }{ 0.06 } =$$

Evaluate

$$\frac{2356933258191963661119456599285093400}{30585627290848204916791848989276401}\approx 77.060157563$$

Solution Steps

Calculate 1.06 to the power of 20 and get 3.2071354722128447318829929845779491454976.

$$\frac{100}{3.2071354722128447318829929845779491454976}+4\left(1-\frac{1}{1.06^{20}}\right)\times \frac{1}{0.06}$$

Expand \frac{100}{3.2071354722128447318829929845779491454976} by multiplying both numerator and the denominator by 10000000000000000000000000000000000000000.

$$\frac{1000000000000000000000000000000000000000000}{32071354722128447318829929845779491454976}+4\left(1-\frac{1}{1.06^{20}}\right)\times \frac{1}{0.06}$$

Reduce the fraction \frac{1000000000000000000000000000000000000000000}{32071354722128447318829929845779491454976} to lowest terms by extracting and canceling out 1048576.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+4\left(1-\frac{1}{1.06^{20}}\right)\times \frac{1}{0.06}$$

Calculate 1.06 to the power of 20 and get 3.2071354722128447318829929845779491454976.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+4\left(1-\frac{1}{3.2071354722128447318829929845779491454976}\right)\times \frac{1}{0.06}$$

Expand \frac{1}{3.2071354722128447318829929845779491454976} by multiplying both numerator and the denominator by 10000000000000000000000000000000000000000.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+4\left(1-\frac{10000000000000000000000000000000000000000}{32071354722128447318829929845779491454976}\right)\times \frac{1}{0.06}$$

Reduce the fraction \frac{10000000000000000000000000000000000000000}{32071354722128447318829929845779491454976} to lowest terms by extracting and canceling out 1048576.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+4\left(1-\frac{9536743164062500000000000000000000}{30585627290848204916791848989276401}\right)\times \frac{1}{0.06}$$

Convert 1 to fraction \frac{30585627290848204916791848989276401}{30585627290848204916791848989276401}.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+4\left(\frac{30585627290848204916791848989276401}{30585627290848204916791848989276401}-\frac{9536743164062500000000000000000000}{30585627290848204916791848989276401}\right)\times \frac{1}{0.06}$$

Since \frac{30585627290848204916791848989276401}{30585627290848204916791848989276401} and \frac{9536743164062500000000000000000000}{30585627290848204916791848989276401} have the same denominator, subtract them by subtracting their numerators.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+4\times \frac{30585627290848204916791848989276401-9536743164062500000000000000000000}{30585627290848204916791848989276401}\times \frac{1}{0.06}$$

Subtract 9536743164062500000000000000000000 from 30585627290848204916791848989276401 to get 21048884126785704916791848989276401.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+4\times \frac{21048884126785704916791848989276401}{30585627290848204916791848989276401}\times \frac{1}{0.06}$$

Express 4\times \frac{21048884126785704916791848989276401}{30585627290848204916791848989276401} as a single fraction.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+\frac{4\times 21048884126785704916791848989276401}{30585627290848204916791848989276401}\times \frac{1}{0.06}$$

Multiply 4 and 21048884126785704916791848989276401 to get 84195536507142819667167395957105604.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+\frac{84195536507142819667167395957105604}{30585627290848204916791848989276401}\times \frac{1}{0.06}$$

Expand \frac{1}{0.06} by multiplying both numerator and the denominator by 100.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+\frac{84195536507142819667167395957105604}{30585627290848204916791848989276401}\times \frac{100}{6}$$

Reduce the fraction \frac{100}{6} to lowest terms by extracting and canceling out 2.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+\frac{84195536507142819667167395957105604}{30585627290848204916791848989276401}\times \frac{50}{3}$$

Multiply \frac{84195536507142819667167395957105604}{30585627290848204916791848989276401} times \frac{50}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+\frac{84195536507142819667167395957105604\times 50}{30585627290848204916791848989276401\times 3}$$

Do the multiplications in the fraction \frac{84195536507142819667167395957105604\times 50}{30585627290848204916791848989276401\times 3}.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+\frac{4209776825357140983358369797855280200}{91756881872544614750375546967829203}$$

Reduce the fraction \frac{4209776825357140983358369797855280200}{91756881872544614750375546967829203} to lowest terms by extracting and canceling out 3.

$$\frac{953674316406250000000000000000000000}{30585627290848204916791848989276401}+\frac{1403258941785713661119456599285093400}{30585627290848204916791848989276401}$$

Since \frac{953674316406250000000000000000000000}{30585627290848204916791848989276401} and \frac{1403258941785713661119456599285093400}{30585627290848204916791848989276401} have the same denominator, add them by adding their numerators.

$$\frac{953674316406250000000000000000000000+1403258941785713661119456599285093400}{30585627290848204916791848989276401}$$

Add 953674316406250000000000000000000000 and 1403258941785713661119456599285093400 to get 2356933258191963661119456599285093400.

$$\frac{2356933258191963661119456599285093400}{30585627290848204916791848989276401}$$