Solve 200{left(1+0.07/4right)}^-16

$$200 { \left(1+ \frac{ 0.07 }{ 4 } \right) }^{ -16 }$$

Evaluate

$$\frac{85899345920000000000000000000000000000000000}{566905339646881866618182176396364175004801}\approx 151.523261315$$

Solution Steps

Expand \frac{0.07}{4} by multiplying both numerator and the denominator by 100.

$$200\left(1+\frac{7}{400}\right)^{-16}$$

Add 1 and \frac{7}{400} to get \frac{407}{400}.

$$200\times \left(\frac{407}{400}\right)^{-16}$$

Calculate \frac{407}{400} to the power of -16 and get \frac{429496729600000000000000000000000000000000}{566905339646881866618182176396364175004801}.

$$200\times \frac{429496729600000000000000000000000000000000}{566905339646881866618182176396364175004801}$$

Multiply 200 and \frac{429496729600000000000000000000000000000000}{566905339646881866618182176396364175004801} to get \frac{85899345920000000000000000000000000000000000}{566905339646881866618182176396364175004801}.

$$\frac{85899345920000000000000000000000000000000000}{566905339646881866618182176396364175004801}$$

Factor

$$\frac{2 ^ {67} \cdot 5 ^ {34}}{11 ^ {16} \cdot 37 ^ {16}} = 151\frac{2.9663963332083862 \times 10^{41}}{5.669053396468819 \times 10^{41}} = 151.52326131467666$$