Solve P_{n}=100,000[(1+20%/12)^240-1/frac{20%{12}}](1+20%/12)

$$P _ { n } = 100,000 [ \frac { ( 1 + \frac { 20 \% } { 12 } ) ^ { 240 } - 1 } { \frac { 20 \% } { 12 } } ] ( 1 + \frac { 20 \% } { 12 } )$$

Solve for P_n

$$P_{n}=\frac{18038085621769432940546195080125973236394287364320473219556734092786448172278792626616809850208789581863989575917136547066392452744911264904566854596413646773863415804107499679641633238603273776462247586177019095402673687992881127164856774940971367861199712461009500869182894165591299522682065339727081363869362626479204930924807884058519193005455673346010499587896530140827976781888952327540949665167026711932339705671561071486461}{57055838483480308012030464533860909525468041277467470669579542370985869323420617694139192366964808034191473811352406055828298273458370594574103225312817151534552107507200375811456379125760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\approx 316147,936849479$$

Assign P_n

$$P_{n}≔\frac{18038085621769432940546195080125973236394287364320473219556734092786448172278792626616809850208789581863989575917136547066392452744911264904566854596413646773863415804107499679641633238603273776462247586177019095402673687992881127164856774940971367861199712461009500869182894165591299522682065339727081363869362626479204930924807884058519193005455673346010499587896530140827976781888952327540949665167026711932339705671561071486461}{57055838483480308012030464533860909525468041277467470669579542370985869323420617694139192366964808034191473811352406055828298273458370594574103225312817151534552107507200375811456379125760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$