Solve 550001.03^6left(1-1.03right)/1.03^6-1

$$55000 \frac{ { 1.03 }^{ 6 } \left( 1-1.03 \right) }{ { 1.03 }^{ 6 } -1 }$$

Evaluate

$$-\frac{656728763090950}{64684098843}\approx -10152.86252476$$

Solution Steps

Calculate 1.03 to the power of 6 and get 1.194052296529.

$$55000\times \frac{1.194052296529\left(1-1.03\right)}{1.03^{6}-1}$$

Subtract 1.03 from 1 to get -0.03.

$$55000\times \frac{1.194052296529\left(-0.03\right)}{1.03^{6}-1}$$

Multiply 1.194052296529 and -0.03 to get -0.03582156889587.

$$55000\times \frac{-0.03582156889587}{1.03^{6}-1}$$

Calculate 1.03 to the power of 6 and get 1.194052296529.

$$55000\times \frac{-0.03582156889587}{1.194052296529-1}$$

Subtract 1 from 1.194052296529 to get 0.194052296529.

$$55000\times \frac{-0.03582156889587}{0.194052296529}$$

Expand \frac{-0.03582156889587}{0.194052296529} by multiplying both numerator and the denominator by 100000000000000.

$$55000\times \frac{-3582156889587}{19405229652900}$$

Reduce the fraction \frac{-3582156889587}{19405229652900} to lowest terms by extracting and canceling out 3.

$$55000\left(-\frac{1194052296529}{6468409884300}\right)$$

Express 55000\left(-\frac{1194052296529}{6468409884300}\right) as a single fraction.

$$\frac{55000\left(-1194052296529\right)}{6468409884300}$$

Multiply 55000 and -1194052296529 to get -65672876309095000.

$$\frac{-65672876309095000}{6468409884300}$$

Reduce the fraction \frac{-65672876309095000}{6468409884300} to lowest terms by extracting and canceling out 100.

$$-\frac{656728763090950}{64684098843}$$

Factor

$$-\frac{656728763090950}{64684098843} = -10152\frac{55791636814}{64684098843} = -10152.862524759747$$