Solve 20*left(1+.010right)^180-1div.010

$$20 \times { \left(1+.010 \right) }^{ 180 } -1 \div .010$$

Evaluate

$$19.91603950712335056324464851240589874730702625087637208795380748166104228523843136826711091941665879459672717177331790538877306093886005151623639568161133556773224665211133819628473012950705764473920168179012194218720756265209381497972419814651206870240882197339890128989618736204395873032285487792046255758304805300299854556303463429153236878945011993042236002$$

Solution Steps

Add 1 and 0.01 to get 1.01.

$$20\times 1.01^{180}-\frac{1}{0.01}$$

Calculate 1.01 to the power of 180 and get 5.995801975356167528162232425620294937365351312543818604397690374083052114261921568413355545970832939729836358588665895269438653046943002575811819784080566778386612332605566909814236506475352882236960084089506097109360378132604690748986209907325603435120441098669945064494809368102197936516142743896023127879152402650149927278151731714576618439472505996521118001.

$$20\times 5.995801975356167528162232425620294937365351312543818604397690374083052114261921568413355545970832939729836358588665895269438653046943002575811819784080566778386612332605566909814236506475352882236960084089506097109360378132604690748986209907325603435120441098669945064494809368102197936516142743896023127879152402650149927278151731714576618439472505996521118001-\frac{1}{0.01}$$

Multiply 20 and 5.995801975356167528162232425620294937365351312543818604397690374083052114261921568413355545970832939729836358588665895269438653046943002575811819784080566778386612332605566909814236506475352882236960084089506097109360378132604690748986209907325603435120441098669945064494809368102197936516142743896023127879152402650149927278151731714576618439472505996521118001 to get 119.91603950712335056324464851240589874730702625087637208795380748166104228523843136826711091941665879459672717177331790538877306093886005151623639568161133556773224665211133819628473012950705764473920168179012194218720756265209381497972419814651206870240882197339890128989618736204395873032285487792046255758304805300299854556303463429153236878945011993042236002.

$$119.91603950712335056324464851240589874730702625087637208795380748166104228523843136826711091941665879459672717177331790538877306093886005151623639568161133556773224665211133819628473012950705764473920168179012194218720756265209381497972419814651206870240882197339890128989618736204395873032285487792046255758304805300299854556303463429153236878945011993042236002-\frac{1}{0.01}$$

Expand \frac{1}{0.01} by multiplying both numerator and the denominator by 100. Anything divided by one gives itself.

$$119.91603950712335056324464851240589874730702625087637208795380748166104228523843136826711091941665879459672717177331790538877306093886005151623639568161133556773224665211133819628473012950705764473920168179012194218720756265209381497972419814651206870240882197339890128989618736204395873032285487792046255758304805300299854556303463429153236878945011993042236002-100$$

Subtract 100 from 119.91603950712335056324464851240589874730702625087637208795380748166104228523843136826711091941665879459672717177331790538877306093886005151623639568161133556773224665211133819628473012950705764473920168179012194218720756265209381497972419814651206870240882197339890128989618736204395873032285487792046255758304805300299854556303463429153236878945011993042236002 to get 19.91603950712335056324464851240589874730702625087637208795380748166104228523843136826711091941665879459672717177331790538877306093886005151623639568161133556773224665211133819628473012950705764473920168179012194218720756265209381497972419814651206870240882197339890128989618736204395873032285487792046255758304805300299854556303463429153236878945011993042236002.

$$19.91603950712335056324464851240589874730702625087637208795380748166104228523843136826711091941665879459672717177331790538877306093886005151623639568161133556773224665211133819628473012950705764473920168179012194218720756265209381497972419814651206870240882197339890128989618736204395873032285487792046255758304805300299854556303463429153236878945011993042236002$$