Solve 60000(1+0.08/12)^-60

$$60000 ( 1 + \frac { 0.08 } { 12 } ) ^ { - 60 }$$

Evaluate

$$\frac{2206108123015981292405819976006758897923987206013407558202743530273437500000000000000000000000000000000000000000000000000000000000000000}{54779345318744703565375910088165738132028462961203048773607069556177503905163509961525725312341354134679944891038592612423251084001}\approx 40272.62666575$$

Solution Steps

Expand \frac{0.08}{12} by multiplying both numerator and the denominator by 100.

$$60000\left(1+\frac{8}{1200}\right)^{-60}$$

Reduce the fraction \frac{8}{1200} to lowest terms by extracting and canceling out 8.

$$60000\left(1+\frac{1}{150}\right)^{-60}$$

Add 1 and \frac{1}{150} to get \frac{151}{150}.

$$60000\times \left(\frac{151}{150}\right)^{-60}$$

Calculate \frac{151}{150} to the power of -60 and get \frac{36768468716933021540096999600112648298733120100223459303379058837890625000000000000000000000000000000000000000000000000000000000000}{54779345318744703565375910088165738132028462961203048773607069556177503905163509961525725312341354134679944891038592612423251084001}.

$$60000\times \frac{36768468716933021540096999600112648298733120100223459303379058837890625000000000000000000000000000000000000000000000000000000000000}{54779345318744703565375910088165738132028462961203048773607069556177503905163509961525725312341354134679944891038592612423251084001}$$

Multiply 60000 and \frac{36768468716933021540096999600112648298733120100223459303379058837890625000000000000000000000000000000000000000000000000000000000000}{54779345318744703565375910088165738132028462961203048773607069556177503905163509961525725312341354134679944891038592612423251084001} to get \frac{2206108123015981292405819976006758897923987206013407558202743530273437500000000000000000000000000000000000000000000000000000000000000000}{54779345318744703565375910088165738132028462961203048773607069556177503905163509961525725312341354134679944891038592612423251084001}.

$$\frac{2206108123015981292405819976006758897923987206013407558202743530273437500000000000000000000000000000000000000000000000000000000000000000}{54779345318744703565375910088165738132028462961203048773607069556177503905163509961525725312341354134679944891038592612423251084001}$$

Factor

$$\frac{2 ^ {65} \cdot 3 ^ {61} \cdot 5 ^ {124}}{151 ^ {60}} = 40272\frac{3.4328339494610836 \times 10^{130}}{5.47793453187447 \times 10^{130}} = 40272.62666574956$$