Solve [10+10/1.05+10/(1.05)^2+10/(1.05)^3]*(1+12/20%)^9

$$[ 10 + \frac { 10 } { 1.05 } + \frac { 10 } { ( 1.05 ) ^ { 2 } } + \frac { 10 } { ( 1.05 ) ^ { 3 } } ] \times ( 1 + \frac { 12 } { 20 } \% ) ^ { 9 }$$

Evaluate

$$\frac{71070884108969755647735974023}{1808789062500000000000000000}\approx 39.291969187$$

Solution Steps

Expand \frac{10}{1.05} by multiplying both numerator and the denominator by 100.

$$\left(10+\frac{1000}{105}+\frac{10}{1.05^{2}}+\frac{10}{1.05^{3}}\right)\left(1+\frac{\frac{12}{20}}{100}\right)^{9}$$

Reduce the fraction \frac{1000}{105} to lowest terms by extracting and canceling out 5.

$$\left(10+\frac{200}{21}+\frac{10}{1.05^{2}}+\frac{10}{1.05^{3}}\right)\left(1+\frac{\frac{12}{20}}{100}\right)^{9}$$

Add 10 and \frac{200}{21} to get \frac{410}{21}.

$$\left(\frac{410}{21}+\frac{10}{1.05^{2}}+\frac{10}{1.05^{3}}\right)\left(1+\frac{\frac{12}{20}}{100}\right)^{9}$$

Calculate 1.05 to the power of 2 and get 1.1025.

$$\left(\frac{410}{21}+\frac{10}{1.1025}+\frac{10}{1.05^{3}}\right)\left(1+\frac{\frac{12}{20}}{100}\right)^{9}$$

Expand \frac{10}{1.1025} by multiplying both numerator and the denominator by 10000.

$$\left(\frac{410}{21}+\frac{100000}{11025}+\frac{10}{1.05^{3}}\right)\left(1+\frac{\frac{12}{20}}{100}\right)^{9}$$

Reduce the fraction \frac{100000}{11025} to lowest terms by extracting and canceling out 25.

$$\left(\frac{410}{21}+\frac{4000}{441}+\frac{10}{1.05^{3}}\right)\left(1+\frac{\frac{12}{20}}{100}\right)^{9}$$

Add \frac{410}{21} and \frac{4000}{441} to get \frac{12610}{441}.

$$\left(\frac{12610}{441}+\frac{10}{1.05^{3}}\right)\left(1+\frac{\frac{12}{20}}{100}\right)^{9}$$

Calculate 1.05 to the power of 3 and get 1.157625.

$$\left(\frac{12610}{441}+\frac{10}{1.157625}\right)\left(1+\frac{\frac{12}{20}}{100}\right)^{9}$$

Expand \frac{10}{1.157625} by multiplying both numerator and the denominator by 1000000.

$$\left(\frac{12610}{441}+\frac{10000000}{1157625}\right)\left(1+\frac{\frac{12}{20}}{100}\right)^{9}$$

Reduce the fraction \frac{10000000}{1157625} to lowest terms by extracting and canceling out 125.

$$\left(\frac{12610}{441}+\frac{80000}{9261}\right)\left(1+\frac{\frac{12}{20}}{100}\right)^{9}$$

Add \frac{12610}{441} and \frac{80000}{9261} to get \frac{344810}{9261}.

$$\frac{344810}{9261}\left(1+\frac{\frac{12}{20}}{100}\right)^{9}$$

Express \frac{\frac{12}{20}}{100} as a single fraction.

$$\frac{344810}{9261}\left(1+\frac{12}{20\times 100}\right)^{9}$$

Multiply 20 and 100 to get 2000.

$$\frac{344810}{9261}\left(1+\frac{12}{2000}\right)^{9}$$

Reduce the fraction \frac{12}{2000} to lowest terms by extracting and canceling out 4.

$$\frac{344810}{9261}\left(1+\frac{3}{500}\right)^{9}$$

Add 1 and \frac{3}{500} to get \frac{503}{500}.

$$\frac{344810}{9261}\times \left(\frac{503}{500}\right)^{9}$$

Calculate \frac{503}{500} to the power of 9 and get \frac{2061160758358799212544183}{1953125000000000000000000}.

$$\frac{344810}{9261}\times \frac{2061160758358799212544183}{1953125000000000000000000}$$

Multiply \frac{344810}{9261} and \frac{2061160758358799212544183}{1953125000000000000000000} to get \frac{71070884108969755647735974023}{1808789062500000000000000000}.

$$\frac{71070884108969755647735974023}{1808789062500000000000000000}$$

Factor

$$\frac{41 \cdot 29 ^ {2} \cdot 503 ^ {9}}{2 ^ {17} \cdot 3 ^ {3} \cdot 5 ^ {26} \cdot 7 ^ {3}} = 39\frac{5.281106714697424 \times 10^{26}}{1.8087890625000003 \times 10^{27}} = 39.29196918668881$$