Solve 160,000(1-0.45/12)^120

$$160,000 ( 1 - \frac { 0.45 } { 12 } ) ^ { 120 }$$

Evaluate

$$1630.0786689443664343117763746728149553185104996534293518955446258206123384506788780668074853156253607713564736139583123197915321113814569795948554922446749012670173866079462413582105851089252989911386078593893520353259422237993261327542656301962547497282293104684063436278374579678102722962826026715325642351234496824769034883825200332033893397159660797143896503456840012809082336015963555006531114474843553403914240299007280073336823879304180451299544074572622776031494140625$$

Solution Steps

Expand \frac{0.45}{12} by multiplying both numerator and the denominator by 100.

$$160000\left(1-\frac{45}{1200}\right)^{120}$$

Reduce the fraction \frac{45}{1200} to lowest terms by extracting and canceling out 15.

$$160000\left(1-\frac{3}{80}\right)^{120}$$

Subtract \frac{3}{80} from 1 to get \frac{77}{80}.

$$160000\times \left(\frac{77}{80}\right)^{120}$$

Calculate \frac{77}{80} to the power of 120 and get \frac{23926932295544591238098248678630380464090399911182517951682669922202292428384893970287953147889747516145115737949163911961560839976316713810875806492372536315626402782314377440102595137469248582453419990835425989256302629727201}{2348542582773833227889480596789337027375682548908319870707290971532209025114608443463698998384768703031934976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$160000\times \frac{23926932295544591238098248678630380464090399911182517951682669922202292428384893970287953147889747516145115737949163911961560839976316713810875806492372536315626402782314377440102595137469248582453419990835425989256302629727201}{2348542582773833227889480596789337027375682548908319870707290971532209025114608443463698998384768703031934976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Multiply 160000 and \frac{23926932295544591238098248678630380464090399911182517951682669922202292428384893970287953147889747516145115737949163911961560839976316713810875806492372536315626402782314377440102595137469248582453419990835425989256302629727201}{2348542582773833227889480596789337027375682548908319870707290971532209025114608443463698998384768703031934976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{23926932295544591238098248678630380464090399911182517951682669922202292428384893970287953147889747516145115737949163911961560839976316713810875806492372536315626402782314377440102595137469248582453419990835425989256302629727201}{14678391142336457674309253729933356421098015930676999191920568572076306406966302771648118739904804393949593600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{23926932295544591238098248678630380464090399911182517951682669922202292428384893970287953147889747516145115737949163911961560839976316713810875806492372536315626402782314377440102595137469248582453419990835425989256302629727201}{14678391142336457674309253729933356421098015930676999191920568572076306406966302771648118739904804393949593600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Factor

$$\frac{7 ^ {120} \cdot 11 ^ {120}}{2 ^ {472} \cdot 5 ^ {116}} = 1630\frac{1.1547335361643867 \times 10^{222}}{1.4678391142336458 \times 10^{223}} = 1630.0786689443664$$