Solve 1500[(1+0.05/12)^12]^4

$$1500 [ ( 1 + \frac { 0.05 } { 12 } ) ^ { 12 } ] ^ { 4 }$$

Evaluate

$$\frac{2171791072681485675582613042868700150345331416441152734239269831856730878648831693150195904057113394690120867288321}{1185900748300287259872090395754116059963483932850655413965667958784000000000000000000000000000000000000000000000}\approx 1831.343032538$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 12 and 4 to get 48.

$$1500\left(1+\frac{0.05}{12}\right)^{48}$$

Expand \frac{0.05}{12} by multiplying both numerator and the denominator by 100.

$$1500\left(1+\frac{5}{1200}\right)^{48}$$

Reduce the fraction \frac{5}{1200} to lowest terms by extracting and canceling out 5.

$$1500\left(1+\frac{1}{240}\right)^{48}$$

Add 1 and \frac{1}{240} to get \frac{241}{240}.

$$1500\times \left(\frac{241}{240}\right)^{48}$$

Calculate \frac{241}{240} to the power of 48 and get \frac{2171791072681485675582613042868700150345331416441152734239269831856730878648831693150195904057113394690120867288321}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000}.

$$1500\times \frac{2171791072681485675582613042868700150345331416441152734239269831856730878648831693150195904057113394690120867288321}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000}$$

Multiply 1500 and \frac{2171791072681485675582613042868700150345331416441152734239269831856730878648831693150195904057113394690120867288321}{1778851122450430889808135593631174089945225899275983120948501938176000000000000000000000000000000000000000000000000} to get \frac{2171791072681485675582613042868700150345331416441152734239269831856730878648831693150195904057113394690120867288321}{1185900748300287259872090395754116059963483932850655413965667958784000000000000000000000000000000000000000000000}.

$$\frac{2171791072681485675582613042868700150345331416441152734239269831856730878648831693150195904057113394690120867288321}{1185900748300287259872090395754116059963483932850655413965667958784000000000000000000000000000000000000000000000}$$

Factor

$$\frac{241 ^ {48}}{2 ^ {190} \cdot 3 ^ {47} \cdot 5 ^ {45}} = 1831\frac{4.068025436600962 \times 10^{110}}{1.185900748300287 \times 10^{111}} = 1831.3430325381303$$