Solve 35*1-1/(1.035)^36/0.035+1000/(1.035)^30

$$35 \times \frac { 1 - \frac { 1 } { ( 1.035 ) ^ { 36 } } } { 0.035 } + \frac { 1000 } { ( 1.035 ) ^ { 30 } }$$

Evaluate

$$\frac{252854787844543599109212979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}\approx 1066.445694024$$

Solution Steps

Calculate 1.035 to the power of 36 and get 3.450266111455967907325786350602725936443778990709405243289294726555537040915296110339113511145114898681640625.

$$35\times \frac{1-\frac{1}{3.450266111455967907325786350602725936443778990709405243289294726555537040915296110339113511145114898681640625}}{0.035}+\frac{1000}{1.035^{30}}$$

Expand \frac{1}{3.450266111455967907325786350602725936443778990709405243289294726555537040915296110339113511145114898681640625} by multiplying both numerator and the denominator by 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$35\times \frac{1-\frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{3450266111455967907325786350602725936443778990709405243289294726555537040915296110339113511145114898681640625}}{0.035}+\frac{1000}{1.035^{30}}$$

Reduce the fraction \frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{3450266111455967907325786350602725936443778990709405243289294726555537040915296110339113511145114898681640625} to lowest terms by extracting and canceling out 14551915228366851806640625.

$$35\times \frac{1-\frac{68719476736000000000000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}}{0.035}+\frac{1000}{1.035^{30}}$$

Convert 1 to fraction \frac{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}.

$$35\times \frac{\frac{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}-\frac{68719476736000000000000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}}{0.035}+\frac{1000}{1.035^{30}}$$

Since \frac{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} and \frac{68719476736000000000000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} have the same denominator, subtract them by subtracting their numerators.

$$35\times \frac{\frac{237100481779207569695836979093150364567632084923980533752615109079380709095164971201-68719476736000000000000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}}{0.035}+\frac{1000}{1.035^{30}}$$

Subtract 68719476736000000000000000000000000000000000000000000000000000000000000000000000000 from 237100481779207569695836979093150364567632084923980533752615109079380709095164971201 to get 168381005043207569695836979093150364567632084923980533752615109079380709095164971201.

$$35\times \frac{\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}}{0.035}+\frac{1000}{1.035^{30}}$$

Express \frac{\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}}{0.035} as a single fraction.

$$35\times \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201\times 0.035}+\frac{1000}{1.035^{30}}$$

Multiply 237100481779207569695836979093150364567632084923980533752615109079380709095164971201 and 0.035 to get 8298516862272264939354294268260262759867122972339318681341528817778324818330773992.035.

$$35\times \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201}{8298516862272264939354294268260262759867122972339318681341528817778324818330773992.035}+\frac{1000}{1.035^{30}}$$

Expand \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201}{8298516862272264939354294268260262759867122972339318681341528817778324818330773992.035} by multiplying both numerator and the denominator by 1000.

$$35\times \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{8298516862272264939354294268260262759867122972339318681341528817778324818330773992035}+\frac{1000}{1.035^{30}}$$

Reduce the fraction \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{8298516862272264939354294268260262759867122972339318681341528817778324818330773992035} to lowest terms by extracting and canceling out 35.

$$35\times \frac{4810885858377359134166770831232867559075202426399443821503288830839448831290427748600}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{1000}{1.035^{30}}$$

Express 35\times \frac{4810885858377359134166770831232867559075202426399443821503288830839448831290427748600}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} as a single fraction.

$$\frac{35\times 4810885858377359134166770831232867559075202426399443821503288830839448831290427748600}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{1000}{1.035^{30}}$$

Multiply 35 and 4810885858377359134166770831232867559075202426399443821503288830839448831290427748600 to get 168381005043207569695836979093150364567632084923980533752615109079380709095164971201000.

$$\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{1000}{1.035^{30}}$$

Calculate 1.035 to the power of 30 and get 2.806793704702633616983891832168892979806961373469044108382206494831711985170841217041015625.

$$\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{1000}{2.806793704702633616983891832168892979806961373469044108382206494831711985170841217041015625}$$

Expand \frac{1000}{2.806793704702633616983891832168892979806961373469044108382206494831711985170841217041015625} by multiplying both numerator and the denominator by 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2806793704702633616983891832168892979806961373469044108382206494831711985170841217041015625}$$

Reduce the fraction \frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2806793704702633616983891832168892979806961373469044108382206494831711985170841217041015625} to lowest terms by extracting and canceling out 931322574615478515625.

$$\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{1073741824000000000000000000000000000000000000000000000000000000000000000}{3013771792079123197504001394491729024198721873046196628470764090905249}$$

Least common multiple of 237100481779207569695836979093150364567632084923980533752615109079380709095164971201 and 3013771792079123197504001394491729024198721873046196628470764090905249 is 237100481779207569695836979093150364567632084923980533752615109079380709095164971201. Convert \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} and \frac{1073741824000000000000000000000000000000000000000000000000000000000000000}{3013771792079123197504001394491729024198721873046196628470764090905249} to fractions with denominator 237100481779207569695836979093150364567632084923980533752615109079380709095164971201.

$$\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{84473782801336029413376000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}$$

Since \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} and \frac{84473782801336029413376000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} have the same denominator, add them by adding their numerators.

$$\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000+84473782801336029413376000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}$$

Add 168381005043207569695836979093150364567632084923980533752615109079380709095164971201000 and 84473782801336029413376000000000000000000000000000000000000000000000000000000000000000 to get 252854787844543599109212979093150364567632084923980533752615109079380709095164971201000.

$$\frac{252854787844543599109212979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}$$