Solve 170*(1+0.03)^20-1/0.03*(1+0.03)^31

$$170 \cdot \frac { ( 1 + 0.03 ) ^ { 20 } - 1 } { 0.03 } \cdot ( 1 + 0.03 ) ^ { 31 }$$

Evaluate

$$11420.276172343397237046541801605960839603951187649214981253289748188617196212996831219234558655641040333$$

Solution Steps

Add 1 and 0.03 to get 1.03.

$$170\times \frac{1.03^{20}-1}{0.03}\left(1+0.03\right)^{31}$$

Calculate 1.03 to the power of 20 and get 1.8061112346694138117573133075817258818401.

$$170\times \frac{1.8061112346694138117573133075817258818401-1}{0.03}\left(1+0.03\right)^{31}$$

Subtract 1 from 1.8061112346694138117573133075817258818401 to get 0.8061112346694138117573133075817258818401.

$$170\times \frac{0.8061112346694138117573133075817258818401}{0.03}\left(1+0.03\right)^{31}$$

Expand \frac{0.8061112346694138117573133075817258818401}{0.03} by multiplying both numerator and the denominator by 10000000000000000000000000000000000000000.

$$170\times \frac{8061112346694138117573133075817258818401}{300000000000000000000000000000000000000}\left(1+0.03\right)^{31}$$

Reduce the fraction \frac{8061112346694138117573133075817258818401}{300000000000000000000000000000000000000} to lowest terms by extracting and canceling out 3.

$$170\times \frac{2687037448898046039191044358605752939467}{100000000000000000000000000000000000000}\left(1+0.03\right)^{31}$$

Multiply 170 and \frac{2687037448898046039191044358605752939467}{100000000000000000000000000000000000000} to get \frac{45679636631266782666247754096297799970939}{10000000000000000000000000000000000000}.

$$\frac{45679636631266782666247754096297799970939}{10000000000000000000000000000000000000}\left(1+0.03\right)^{31}$$

Add 1 and 0.03 to get 1.03.

$$\frac{45679636631266782666247754096297799970939}{10000000000000000000000000000000000000}\times 1.03^{31}$$

Calculate 1.03 to the power of 31 and get 2.50008034532535014880175427460595041962781023619801764790645847.

$$\frac{45679636631266782666247754096297799970939}{10000000000000000000000000000000000000}\times 2.50008034532535014880175427460595041962781023619801764790645847$$

Multiply \frac{45679636631266782666247754096297799970939}{10000000000000000000000000000000000000} and 2.50008034532535014880175427460595041962781023619801764790645847 to get \frac{11420276172343397237046541801605960839603951187649214981253289748188617196212996831219234558655641040333}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{11420276172343397237046541801605960839603951187649214981253289748188617196212996831219234558655641040333}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Factor

$$\frac{7 \cdot 11 \cdot 17 \cdot 29 \cdot 37 \cdot 41 \cdot 557 \cdot 641 \cdot 165941 \cdot 291041 \cdot 48264871 \cdot 953119081 \cdot 103 ^ {31}}{2 ^ {99} \cdot 5 ^ {99}} = 11420\frac{2.761723433984292 \times 10^{98}}{1 \times 10^{99}} = 11420.276172343398$$