Solve [900*(1+0.05)^7+600*((1+0.05)^2-1/0.05)*(1+0.05)^3-700]

$$[ 900 \times ( 1 + 0.05 ) ^ { 7 } + 600 \times ( \frac { ( 1 + 0.05 ) ^ { 2 } - 1 } { 0.05 } ) \times ( 1 + 0.05 ) ^ { 3 } - 700 ]$$

Evaluate

$$1990.269130390625$$

Solution Steps

Add 1 and 0.05 to get 1.05.

$$900\times 1.05^{7}+600\times \frac{\left(1+0.05\right)^{2}-1}{0.05}\left(1+0.05\right)^{3}-700$$

Calculate 1.05 to the power of 7 and get 1.40710042265625.

$$900\times 1.40710042265625+600\times \frac{\left(1+0.05\right)^{2}-1}{0.05}\left(1+0.05\right)^{3}-700$$

Multiply 900 and 1.40710042265625 to get 1266.390380390625.

$$1266.390380390625+600\times \frac{\left(1+0.05\right)^{2}-1}{0.05}\left(1+0.05\right)^{3}-700$$

Add 1 and 0.05 to get 1.05.

$$1266.390380390625+600\times \frac{1.05^{2}-1}{0.05}\left(1+0.05\right)^{3}-700$$

Calculate 1.05 to the power of 2 and get 1.1025.

$$1266.390380390625+600\times \frac{1.1025-1}{0.05}\left(1+0.05\right)^{3}-700$$

Subtract 1 from 1.1025 to get 0.1025.

$$1266.390380390625+600\times \frac{0.1025}{0.05}\left(1+0.05\right)^{3}-700$$

Expand \frac{0.1025}{0.05} by multiplying both numerator and the denominator by 10000.

$$1266.390380390625+600\times \frac{1025}{500}\left(1+0.05\right)^{3}-700$$

Reduce the fraction \frac{1025}{500} to lowest terms by extracting and canceling out 25.

$$1266.390380390625+600\times \frac{41}{20}\left(1+0.05\right)^{3}-700$$

Multiply 600 and \frac{41}{20} to get 1230.

$$1266.390380390625+1230\left(1+0.05\right)^{3}-700$$

Add 1 and 0.05 to get 1.05.

$$1266.390380390625+1230\times 1.05^{3}-700$$

Calculate 1.05 to the power of 3 and get 1.157625.

$$1266.390380390625+1230\times 1.157625-700$$

Multiply 1230 and 1.157625 to get 1423.87875.

$$1266.390380390625+1423.87875-700$$

Add 1266.390380390625 and 1423.87875 to get 2690.269130390625.

$$2690.269130390625-700$$

Subtract 700 from 2690.269130390625 to get 1990.269130390625.

$$1990.269130390625$$

Factor

$$\frac{7 \cdot 37 \cdot 4339 \cdot 22669}{2 ^ {12} \cdot 5 ^ {5}} = 1990\frac{3444869}{12800000} = 1990.269130390625$$