Solve 1200000(1+0.05/12)*1+(1+0.05/12)^-180/frac{0.05{12}}

$$1200000 ( 1 + \frac { 0.05 } { 12 } ) \times \frac { 1 + ( 1 + \frac { 0.05 } { 12 } ) ^ { - 180 } } { \frac { 0.05 } { 12 } }$$

Evaluate

$$\frac{1024429483851890279205238869971373621918425501132808949871607906612076722198081857266114321842542297368250180842305499673401084590101547196021841997915328770977101591501538858957912131499026304854113416595805645455660095810643641438502669338441044157378691525079148737021453328217535373419332917981858996279103114165654827151779809378261142410684742102156929591392106568618746491849674710945868516802797991486124952899272887783041200000}{2404643066303023591984276415944893295832741495577965241986523375457684620238377249438216821793907238735277577606804127552203623088759451404654536022144664034626298120200823340907823844654465149783843595848268857749651275828572617472776662651243510740590219657950030211000875962024672798822036369231877580494824046215957216984024237130916813314954156646462412141743107083743936693809386967309365549110643124087568993427637924561}\approx 426021432.539209016$$

Solution Steps

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

$$1200000\left(1+\frac{5}{1200}\right)\times \frac{1+\left(1+\frac{0.05}{12}\right)^{-180}}{\frac{0.05}{12}}$$

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

$$1200000\left(1+\frac{1}{240}\right)\times \frac{1+\left(1+\frac{0.05}{12}\right)^{-180}}{\frac{0.05}{12}}$$

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

$$1200000\times \frac{241}{240}\times \frac{1+\left(1+\frac{0.05}{12}\right)^{-180}}{\frac{0.05}{12}}$$

Multiply 1200000 and \frac{241}{240} to get 1205000.

$$1205000\times \frac{1+\left(1+\frac{0.05}{12}\right)^{-180}}{\frac{0.05}{12}}$$

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

$$1205000\times \frac{1+\left(1+\frac{5}{1200}\right)^{-180}}{\frac{0.05}{12}}$$

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

$$1205000\times \frac{1+\left(1+\frac{1}{240}\right)^{-180}}{\frac{0.05}{12}}$$

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

$$1205000\times \frac{1+\left(\frac{241}{240}\right)^{-180}}{\frac{0.05}{12}}$$

Calculate \frac{241}{240} to the power of -180 and get \frac{274172257564213213669488442066758733969663883843051168240921122024761941687619297273818347483120269938339921165348121654419830660693594874829791816925909943469313479282883957306141229687462486280521540563738576495384122367517033721146382083084517376000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}.

$$1205000\times \frac{1+\frac{274172257564213213669488442066758733969663883843051168240921122024761941687619297273818347483120269938339921165348121654419830660693594874829791816925909943469313479282883957306141229687462486280521540563738576495384122367517033721146382083084517376000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}}{\frac{0.05}{12}}$$

Add 1 and \frac{274172257564213213669488442066758733969663883843051168240921122024761941687619297273818347483120269938339921165348121654419830660693594874829791816925909943469313479282883957306141229687462486280521540563738576495384122367517033721146382083084517376000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201} to get \frac{853691236543241899337699058309478018265354584277340791559673255510063935165068214388428601535451914473541817368587916394500903825084622663351534998262773975814251326251282382464926776249188587378427847163171371213050079842203034532085557782034203464482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}.

$$1205000\times \frac{\frac{853691236543241899337699058309478018265354584277340791559673255510063935165068214388428601535451914473541817368587916394500903825084622663351534998262773975814251326251282382464926776249188587378427847163171371213050079842203034532085557782034203464482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}}{\frac{0.05}{12}}$$

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

$$1205000\times \frac{\frac{853691236543241899337699058309478018265354584277340791559673255510063935165068214388428601535451914473541817368587916394500903825084622663351534998262773975814251326251282382464926776249188587378427847163171371213050079842203034532085557782034203464482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}}{\frac{5}{1200}}$$

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

$$1205000\times \frac{\frac{853691236543241899337699058309478018265354584277340791559673255510063935165068214388428601535451914473541817368587916394500903825084622663351534998262773975814251326251282382464926776249188587378427847163171371213050079842203034532085557782034203464482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}}{\frac{1}{240}}$$

Divide \frac{853691236543241899337699058309478018265354584277340791559673255510063935165068214388428601535451914473541817368587916394500903825084622663351534998262773975814251326251282382464926776249188587378427847163171371213050079842203034532085557782034203464482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201} by \frac{1}{240} by multiplying \frac{853691236543241899337699058309478018265354584277340791559673255510063935165068214388428601535451914473541817368587916394500903825084622663351534998262773975814251326251282382464926776249188587378427847163171371213050079842203034532085557782034203464482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201} by the reciprocal of \frac{1}{240}.

$$1205000\times \frac{853691236543241899337699058309478018265354584277340791559673255510063935165068214388428601535451914473541817368587916394500903825084622663351534998262773975814251326251282382464926776249188587378427847163171371213050079842203034532085557782034203464482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}\times 240$$

Multiply \frac{853691236543241899337699058309478018265354584277340791559673255510063935165068214388428601535451914473541817368587916394500903825084622663351534998262773975814251326251282382464926776249188587378427847163171371213050079842203034532085557782034203464482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201} and 240 to get \frac{204885896770378055841047773994274724383685100226561789974321581322415344439616371453222864368508459473650036168461099934680216918020309439204368399583065754195420318300307771791582426299805260970822683319161129091132019162128728287700533867688208831475738305015829747404290665643507074683866583596371799255820622833130965430355961875652228482136948420431385918278421313723749298369934942189173703360559598297224990579854577556608240}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}.

$$1205000\times \frac{204885896770378055841047773994274724383685100226561789974321581322415344439616371453222864368508459473650036168461099934680216918020309439204368399583065754195420318300307771791582426299805260970822683319161129091132019162128728287700533867688208831475738305015829747404290665643507074683866583596371799255820622833130965430355961875652228482136948420431385918278421313723749298369934942189173703360559598297224990579854577556608240}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201}$$

Multiply 1205000 and \frac{204885896770378055841047773994274724383685100226561789974321581322415344439616371453222864368508459473650036168461099934680216918020309439204368399583065754195420318300307771791582426299805260970822683319161129091132019162128728287700533867688208831475738305015829747404290665643507074683866583596371799255820622833130965430355961875652228482136948420431385918278421313723749298369934942189173703360559598297224990579854577556608240}{579518978979028685668210616242719284295690700434289623318752133485301993477448917114610254052331644535201896203239794740081073164391027788521743181336864032344937846968398425158785546561726101097906306599432794717665957474686000810939175698949686088482242937565957280851211106847946144516110764984882496899252595138045689293149841148550952008903951751797441326160088807182288743208062259121557097335664992905104127416060739819201} to get \frac{1024429483851890279205238869971373621918425501132808949871607906612076722198081857266114321842542297368250180842305499673401084590101547196021841997915328770977101591501538858957912131499026304854113416595805645455660095810643641438502669338441044157378691525079148737021453328217535373419332917981858996279103114165654827151779809378261142410684742102156929591392106568618746491849674710945868516802797991486124952899272887783041200000}{2404643066303023591984276415944893295832741495577965241986523375457684620238377249438216821793907238735277577606804127552203623088759451404654536022144664034626298120200823340907823844654465149783843595848268857749651275828572617472776662651243510740590219657950030211000875962024672798822036369231877580494824046215957216984024237130916813314954156646462412141743107083743936693809386967309365549110643124087568993427637924561}.

$$\frac{1024429483851890279205238869971373621918425501132808949871607906612076722198081857266114321842542297368250180842305499673401084590101547196021841997915328770977101591501538858957912131499026304854113416595805645455660095810643641438502669338441044157378691525079148737021453328217535373419332917981858996279103114165654827151779809378261142410684742102156929591392106568618746491849674710945868516802797991486124952899272887783041200000}{2404643066303023591984276415944893295832741495577965241986523375457684620238377249438216821793907238735277577606804127552203623088759451404654536022144664034626298120200823340907823844654465149783843595848268857749651275828572617472776662651243510740590219657950030211000875962024672798822036369231877580494824046215957216984024237130916813314954156646462412141743107083743936693809386967309365549110643124087568993427637924561}$$