Solve 15*(1-1/1.04^18/0.04)+1000/1.04^18

$$15 \times ( \frac{ 1- \frac{ 1 }{ { 1.04 }^{ 18 } } }{ 0.04 } )+ \frac{ 1000 }{ { 1.04 }^{ 18 } }$$

Evaluate

$$\frac{20149763342734501953303606625}{29479510200013918864408576}\approx 683.517575632$$

Solution Steps

Calculate 1.04 to the power of 18 and get 2.025816515378531204278916676830887936.

$$15\times \frac{1-\frac{1}{2.025816515378531204278916676830887936}}{0.04}+\frac{1000}{1.04^{18}}$$

Expand \frac{1}{2.025816515378531204278916676830887936} by multiplying both numerator and the denominator by 1000000000000000000000000000000000000.

$$15\times \frac{1-\frac{1000000000000000000000000000000000000}{2025816515378531204278916676830887936}}{0.04}+\frac{1000}{1.04^{18}}$$

Reduce the fraction \frac{1000000000000000000000000000000000000}{2025816515378531204278916676830887936} to lowest terms by extracting and canceling out 68719476736.

$$15\times \frac{1-\frac{14551915228366851806640625}{29479510200013918864408576}}{0.04}+\frac{1000}{1.04^{18}}$$

Convert 1 to fraction \frac{29479510200013918864408576}{29479510200013918864408576}.

$$15\times \frac{\frac{29479510200013918864408576}{29479510200013918864408576}-\frac{14551915228366851806640625}{29479510200013918864408576}}{0.04}+\frac{1000}{1.04^{18}}$$

Since \frac{29479510200013918864408576}{29479510200013918864408576} and \frac{14551915228366851806640625}{29479510200013918864408576} have the same denominator, subtract them by subtracting their numerators.

$$15\times \frac{\frac{29479510200013918864408576-14551915228366851806640625}{29479510200013918864408576}}{0.04}+\frac{1000}{1.04^{18}}$$

Subtract 14551915228366851806640625 from 29479510200013918864408576 to get 14927594971647067057767951.

$$15\times \frac{\frac{14927594971647067057767951}{29479510200013918864408576}}{0.04}+\frac{1000}{1.04^{18}}$$

Express \frac{\frac{14927594971647067057767951}{29479510200013918864408576}}{0.04} as a single fraction.

$$15\times \frac{14927594971647067057767951}{29479510200013918864408576\times 0.04}+\frac{1000}{1.04^{18}}$$

Multiply 29479510200013918864408576 and 0.04 to get 1179180408000556754576343.04.

$$15\times \frac{14927594971647067057767951}{1179180408000556754576343.04}+\frac{1000}{1.04^{18}}$$

Expand \frac{14927594971647067057767951}{1179180408000556754576343.04} by multiplying both numerator and the denominator by 100.

$$15\times \frac{1492759497164706705776795100}{117918040800055675457634304}+\frac{1000}{1.04^{18}}$$

Reduce the fraction \frac{1492759497164706705776795100}{117918040800055675457634304} to lowest terms by extracting and canceling out 4.

$$15\times \frac{373189874291176676444198775}{29479510200013918864408576}+\frac{1000}{1.04^{18}}$$

Express 15\times \frac{373189874291176676444198775}{29479510200013918864408576} as a single fraction.

$$\frac{15\times 373189874291176676444198775}{29479510200013918864408576}+\frac{1000}{1.04^{18}}$$

Multiply 15 and 373189874291176676444198775 to get 5597848114367650146662981625.

$$\frac{5597848114367650146662981625}{29479510200013918864408576}+\frac{1000}{1.04^{18}}$$

Calculate 1.04 to the power of 18 and get 2.025816515378531204278916676830887936.

$$\frac{5597848114367650146662981625}{29479510200013918864408576}+\frac{1000}{2.025816515378531204278916676830887936}$$

Expand \frac{1000}{2.025816515378531204278916676830887936} by multiplying both numerator and the denominator by 1000000000000000000000000000000000000.

$$\frac{5597848114367650146662981625}{29479510200013918864408576}+\frac{1000000000000000000000000000000000000000}{2025816515378531204278916676830887936}$$

Reduce the fraction \frac{1000000000000000000000000000000000000000}{2025816515378531204278916676830887936} to lowest terms by extracting and canceling out 549755813888.

$$\frac{5597848114367650146662981625}{29479510200013918864408576}+\frac{1818989403545856475830078125}{3684938775001739858051072}$$

Least common multiple of 29479510200013918864408576 and 3684938775001739858051072 is 29479510200013918864408576. Convert \frac{5597848114367650146662981625}{29479510200013918864408576} and \frac{1818989403545856475830078125}{3684938775001739858051072} to fractions with denominator 29479510200013918864408576.

$$\frac{5597848114367650146662981625}{29479510200013918864408576}+\frac{14551915228366851806640625000}{29479510200013918864408576}$$

Since \frac{5597848114367650146662981625}{29479510200013918864408576} and \frac{14551915228366851806640625000}{29479510200013918864408576} have the same denominator, add them by adding their numerators.

$$\frac{5597848114367650146662981625+14551915228366851806640625000}{29479510200013918864408576}$$

Add 5597848114367650146662981625 and 14551915228366851806640625000 to get 20149763342734501953303606625.

$$\frac{20149763342734501953303606625}{29479510200013918864408576}$$

Factor

$$\frac{9781 \cdot 26839 \cdot 614059348526942567 \cdot 5 ^ {3}}{2 ^ {18} \cdot 13 ^ {18}} = 683\frac{1.5257876124997387 \times 10^{25}}{2.947951020001392 \times 10^{25}} = 683.5175756320738$$