Solve 15*1-1/(1+2%)^60/0.02+100/(1.02)^60

$$15 \times \frac { 1 - \frac { 1 } { ( 1 + 2 \% ) ^ { 60 } } } { 0.02 } + \frac { 100 } { ( 1.02 ) ^ { 60 } }$$

Evaluate

$$\frac{1570595295550101317731761790119048900197780082986481663525693640682531983656662677206925372487125508500750}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}\approx 551.891526802$$

Solution Steps

Reduce the fraction \frac{2}{100} to lowest terms by extracting and canceling out 2.

$$15\times \frac{1-\frac{1}{\left(1+\frac{1}{50}\right)^{60}}}{0.02}+\frac{100}{1.02^{60}}$$

Add 1 and \frac{1}{50} to get \frac{51}{50}.

$$15\times \frac{1-\frac{1}{\left(\frac{51}{50}\right)^{60}}}{0.02}+\frac{100}{1.02^{60}}$$

Calculate \frac{51}{50} to the power of 60 and get \frac{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000}.

$$15\times \frac{1-\frac{1}{\frac{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000}}}{0.02}+\frac{100}{1.02^{60}}$$

Divide 1 by \frac{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000} by multiplying 1 by the reciprocal of \frac{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000}.

$$15\times \frac{1-1\times \frac{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}}{0.02}+\frac{100}{1.02^{60}}$$

Multiply 1 and \frac{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001} to get \frac{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}.

$$15\times \frac{1-\frac{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}}{0.02}+\frac{100}{1.02^{60}}$$

Subtract \frac{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001} from 1 to get \frac{1978478829001681284014887421399271417711623443981975551367591520910042644875550236275900496649500678001}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}.

$$15\times \frac{\frac{1978478829001681284014887421399271417711623443981975551367591520910042644875550236275900496649500678001}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}}{0.02}+\frac{100}{1.02^{60}}$$

Express \frac{\frac{1978478829001681284014887421399271417711623443981975551367591520910042644875550236275900496649500678001}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}}{0.02} as a single fraction.

$$15\times \frac{1978478829001681284014887421399271417711623443981975551367591520910042644875550236275900496649500678001}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001\times 0.02}+\frac{100}{1.02^{60}}$$

Multiply 2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001 and 0.02 to get 56916811339801696624416993241904495737044968879639511027351830418200852897511004725518009932990013560.02.

$$15\times \frac{1978478829001681284014887421399271417711623443981975551367591520910042644875550236275900496649500678001}{56916811339801696624416993241904495737044968879639511027351830418200852897511004725518009932990013560.02}+\frac{100}{1.02^{60}}$$

Expand \frac{1978478829001681284014887421399271417711623443981975551367591520910042644875550236275900496649500678001}{56916811339801696624416993241904495737044968879639511027351830418200852897511004725518009932990013560.02} by multiplying both numerator and the denominator by 100.

$$15\times \frac{197847882900168128401488742139927141771162344398197555136759152091004264487555023627590049664950067800100}{5691681133980169662441699324190449573704496887963951102735183041820085289751100472551800993299001356002}+\frac{100}{1.02^{60}}$$

Reduce the fraction \frac{197847882900168128401488742139927141771162344398197555136759152091004264487555023627590049664950067800100}{5691681133980169662441699324190449573704496887963951102735183041820085289751100472551800993299001356002} to lowest terms by extracting and canceling out 2.

$$15\times \frac{98923941450084064200744371069963570885581172199098777568379576045502132243777511813795024832475033900050}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}+\frac{100}{1.02^{60}}$$

Multiply 15 and \frac{98923941450084064200744371069963570885581172199098777568379576045502132243777511813795024832475033900050}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001} to get \frac{494619707250420321003721855349817854427905860995493887841897880227510661218887559068975124162375169500250}{948613522330028277073616554031741595617416147993991850455863840303347548291850078758633498883166892667}.

$$\frac{494619707250420321003721855349817854427905860995493887841897880227510661218887559068975124162375169500250}{948613522330028277073616554031741595617416147993991850455863840303347548291850078758633498883166892667}+\frac{100}{1.02^{60}}$$

Calculate 1.02 to the power of 60 and get \frac{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000}.

$$\frac{494619707250420321003721855349817854427905860995493887841897880227510661218887559068975124162375169500250}{948613522330028277073616554031741595617416147993991850455863840303347548291850078758633498883166892667}+\frac{100}{\frac{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000}}$$

Divide 100 by \frac{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000} by multiplying 100 by the reciprocal of \frac{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000}.

$$\frac{494619707250420321003721855349817854427905860995493887841897880227510661218887559068975124162375169500250}{948613522330028277073616554031741595617416147993991850455863840303347548291850078758633498883166892667}+100\times \frac{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}$$

Multiply 100 and \frac{867361737988403547205962240695953369140625000000000000000000000000000000000000000000000000000000000000}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001} to get \frac{86736173798840354720596224069595336914062500000000000000000000000000000000000000000000000000000000000000}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}.

$$\frac{494619707250420321003721855349817854427905860995493887841897880227510661218887559068975124162375169500250}{948613522330028277073616554031741595617416147993991850455863840303347548291850078758633498883166892667}+\frac{86736173798840354720596224069595336914062500000000000000000000000000000000000000000000000000000000000000}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}$$

Add \frac{494619707250420321003721855349817854427905860995493887841897880227510661218887559068975124162375169500250}{948613522330028277073616554031741595617416147993991850455863840303347548291850078758633498883166892667} and \frac{86736173798840354720596224069595336914062500000000000000000000000000000000000000000000000000000000000000}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001} to get \frac{1570595295550101317731761790119048900197780082986481663525693640682531983656662677206925372487125508500750}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}.

$$\frac{1570595295550101317731761790119048900197780082986481663525693640682531983656662677206925372487125508500750}{2845840566990084831220849662095224786852248443981975551367591520910042644875550236275900496649500678001}$$