Solve 150000(1+6%/12)^48

$$150000 ( 1 + \frac { 6 \% } { 12 } ) ^ { 48 }$$

Evaluate

$$\frac{1072832721091396319641087709737998888357690671003002695809211601848402417135367783189853840228059850239239388803}{5629499534213120000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\approx 190573.374164308$$

Solution Steps

Express \frac{\frac{6}{100}}{12} as a single fraction.

$$150000\left(1+\frac{6}{100\times 12}\right)^{48}$$

Multiply 100 and 12 to get 1200.

$$150000\left(1+\frac{6}{1200}\right)^{48}$$

Reduce the fraction \frac{6}{1200} to lowest terms by extracting and canceling out 6.

$$150000\left(1+\frac{1}{200}\right)^{48}$$

Add 1 and \frac{1}{200} to get \frac{201}{200}.

$$150000\times \left(\frac{201}{200}\right)^{48}$$

Calculate \frac{201}{200} to the power of 48 and get \frac{357610907030465439880362569912666296119230223667667565269737200616134139045122594396617946742686616746413129601}{281474976710656000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$150000\times \frac{357610907030465439880362569912666296119230223667667565269737200616134139045122594396617946742686616746413129601}{281474976710656000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Multiply 150000 and \frac{357610907030465439880362569912666296119230223667667565269737200616134139045122594396617946742686616746413129601}{281474976710656000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{1072832721091396319641087709737998888357690671003002695809211601848402417135367783189853840228059850239239388803}{5629499534213120000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{1072832721091396319641087709737998888357690671003002695809211601848402417135367783189853840228059850239239388803}{5629499534213120000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Factor

$$\frac{3 ^ {49} \cdot 67 ^ {48}}{2 ^ {140} \cdot 5 ^ {91}} = 190573\frac{2.1063577993993228 \times 10^{105}}{5.629499534213121 \times 10^{105}} = 190573.3741643083$$