Solve 1000*0.075/2left(1-left(1+.07695div2right)^-44right)/.07695div2+1000/left(1+.07695div2right)^44

$$\frac{ \frac{ 1000 \cdot 0.075 }{ 2 } \left( 1- { \left(1+.07695 \div 2 \right) }^{ -44 } \right) }{ .07695 \div 2 } + \frac{ 1000 }{ { \left(1+.07695 \div 2 \right) }^{ 44 } }$$

Evaluate

$$\frac{159609055344292807849099926888186639629762460783631819674990330449993092747148151712779346455547025504296617968174505933098834575687480070657607314573158634318579034399949163134718214043234989746643128500000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}\approx 979.471693258$$

Solution Steps

Multiply 1000 and 0.075 to get 75.

$$\frac{\frac{75}{2}\left(1-\left(1+\frac{0.07695}{2}\right)^{-44}\right)}{\frac{0.07695}{2}}+\frac{1000}{\left(1+\frac{0.07695}{2}\right)^{44}}$$

Expand \frac{0.07695}{2} by multiplying both numerator and the denominator by 100000.

$$\frac{\frac{75}{2}\left(1-\left(1+\frac{7695}{200000}\right)^{-44}\right)}{\frac{0.07695}{2}}+\frac{1000}{\left(1+\frac{0.07695}{2}\right)^{44}}$$

Reduce the fraction \frac{7695}{200000} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{75}{2}\left(1-\left(1+\frac{1539}{40000}\right)^{-44}\right)}{\frac{0.07695}{2}}+\frac{1000}{\left(1+\frac{0.07695}{2}\right)^{44}}$$

Add 1 and \frac{1539}{40000} to get \frac{41539}{40000}.

$$\frac{\frac{75}{2}\left(1-\left(\frac{41539}{40000}\right)^{-44}\right)}{\frac{0.07695}{2}}+\frac{1000}{\left(1+\frac{0.07695}{2}\right)^{44}}$$

Calculate \frac{41539}{40000} to the power of -44 and get \frac{30948500982134506872478105600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}.

$$\frac{\frac{75}{2}\left(1-\frac{30948500982134506872478105600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}\right)}{\frac{0.07695}{2}}+\frac{1000}{\left(1+\frac{0.07695}{2}\right)^{44}}$$

Subtract \frac{30948500982134506872478105600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841} from 1 to get \frac{132005728775574416802013988641679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}.

$$\frac{\frac{75}{2}\times \frac{132005728775574416802013988641679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}}{\frac{0.07695}{2}}+\frac{1000}{\left(1+\frac{0.07695}{2}\right)^{44}}$$

Multiply \frac{75}{2} and \frac{132005728775574416802013988641679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841} to get \frac{9900429658168081260151049148125961919510221357300468523990505928126968486893050274298370709754343612555624752651028231551955320599151591437102882856404556910814656697076088103216566570626932461004188738075}{325908459515417847348984188483358984520272569528012493973080158083385826317148007314623218926782496334816660070694086174718808549310709104989410209504121517621724178588695682752441775216718198960111699682}.

$$\frac{\frac{9900429658168081260151049148125961919510221357300468523990505928126968486893050274298370709754343612555624752651028231551955320599151591437102882856404556910814656697076088103216566570626932461004188738075}{325908459515417847348984188483358984520272569528012493973080158083385826317148007314623218926782496334816660070694086174718808549310709104989410209504121517621724178588695682752441775216718198960111699682}}{\frac{0.07695}{2}}+\frac{1000}{\left(1+\frac{0.07695}{2}\right)^{44}}$$

Expand \frac{0.07695}{2} by multiplying both numerator and the denominator by 100000.

$$\frac{\frac{9900429658168081260151049148125961919510221357300468523990505928126968486893050274298370709754343612555624752651028231551955320599151591437102882856404556910814656697076088103216566570626932461004188738075}{325908459515417847348984188483358984520272569528012493973080158083385826317148007314623218926782496334816660070694086174718808549310709104989410209504121517621724178588695682752441775216718198960111699682}}{\frac{7695}{200000}}+\frac{1000}{\left(1+\frac{0.07695}{2}\right)^{44}}$$

Reduce the fraction \frac{7695}{200000} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{9900429658168081260151049148125961919510221357300468523990505928126968486893050274298370709754343612555624752651028231551955320599151591437102882856404556910814656697076088103216566570626932461004188738075}{325908459515417847348984188483358984520272569528012493973080158083385826317148007314623218926782496334816660070694086174718808549310709104989410209504121517621724178588695682752441775216718198960111699682}}{\frac{1539}{40000}}+\frac{1000}{\left(1+\frac{0.07695}{2}\right)^{44}}$$

Divide \frac{9900429658168081260151049148125961919510221357300468523990505928126968486893050274298370709754343612555624752651028231551955320599151591437102882856404556910814656697076088103216566570626932461004188738075}{325908459515417847348984188483358984520272569528012493973080158083385826317148007314623218926782496334816660070694086174718808549310709104989410209504121517621724178588695682752441775216718198960111699682} by \frac{1539}{40000} by multiplying \frac{9900429658168081260151049148125961919510221357300468523990505928126968486893050274298370709754343612555624752651028231551955320599151591437102882856404556910814656697076088103216566570626932461004188738075}{325908459515417847348984188483358984520272569528012493973080158083385826317148007314623218926782496334816660070694086174718808549310709104989410209504121517621724178588695682752441775216718198960111699682} by the reciprocal of \frac{1539}{40000}.

$$\frac{9900429658168081260151049148125961919510221357300468523990505928126968486893050274298370709754343612555624752651028231551955320599151591437102882856404556910814656697076088103216566570626932461004188738075}{325908459515417847348984188483358984520272569528012493973080158083385826317148007314623218926782496334816660070694086174718808549310709104989410209504121517621724178588695682752441775216718198960111699682}\times \frac{40000}{1539}+\frac{1000}{\left(1+\frac{0.07695}{2}\right)^{44}}$$

Multiply \frac{9900429658168081260151049148125961919510221357300468523990505928126968486893050274298370709754343612555624752651028231551955320599151591437102882856404556910814656697076088103216566570626932461004188738075}{325908459515417847348984188483358984520272569528012493973080158083385826317148007314623218926782496334816660070694086174718808549310709104989410209504121517621724178588695682752441775216718198960111699682} and \frac{40000}{1539} to get \frac{128660554362158300976621821288186639629762460783631819674990330449993092747148151712779346455547025504296617968174505933098834575687480070657607314573158634318579034399949163134718214043234989746643128500000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}.

$$\frac{128660554362158300976621821288186639629762460783631819674990330449993092747148151712779346455547025504296617968174505933098834575687480070657607314573158634318579034399949163134718214043234989746643128500000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}+\frac{1000}{\left(1+\frac{0.07695}{2}\right)^{44}}$$

Expand \frac{0.07695}{2} by multiplying both numerator and the denominator by 100000.

$$\frac{128660554362158300976621821288186639629762460783631819674990330449993092747148151712779346455547025504296617968174505933098834575687480070657607314573158634318579034399949163134718214043234989746643128500000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}+\frac{1000}{\left(1+\frac{7695}{200000}\right)^{44}}$$

Reduce the fraction \frac{7695}{200000} to lowest terms by extracting and canceling out 5.

$$\frac{128660554362158300976621821288186639629762460783631819674990330449993092747148151712779346455547025504296617968174505933098834575687480070657607314573158634318579034399949163134718214043234989746643128500000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}+\frac{1000}{\left(1+\frac{1539}{40000}\right)^{44}}$$

Add 1 and \frac{1539}{40000} to get \frac{41539}{40000}.

$$\frac{128660554362158300976621821288186639629762460783631819674990330449993092747148151712779346455547025504296617968174505933098834575687480070657607314573158634318579034399949163134718214043234989746643128500000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}+\frac{1000}{\left(\frac{41539}{40000}\right)^{44}}$$

Calculate \frac{41539}{40000} to the power of 44 and get \frac{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}{30948500982134506872478105600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{128660554362158300976621821288186639629762460783631819674990330449993092747148151712779346455547025504296617968174505933098834575687480070657607314573158634318579034399949163134718214043234989746643128500000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}+\frac{1000}{\frac{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}{30948500982134506872478105600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}$$

Divide 1000 by \frac{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}{30948500982134506872478105600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by multiplying 1000 by the reciprocal of \frac{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}{30948500982134506872478105600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{128660554362158300976621821288186639629762460783631819674990330449993092747148151712779346455547025504296617968174505933098834575687480070657607314573158634318579034399949163134718214043234989746643128500000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}+1000\times \frac{30948500982134506872478105600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}$$

Multiply 1000 and \frac{30948500982134506872478105600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841} to get \frac{30948500982134506872478105600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}.

$$\frac{128660554362158300976621821288186639629762460783631819674990330449993092747148151712779346455547025504296617968174505933098834575687480070657607314573158634318579034399949163134718214043234989746643128500000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}+\frac{30948500982134506872478105600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}$$

Add \frac{128660554362158300976621821288186639629762460783631819674990330449993092747148151712779346455547025504296617968174505933098834575687480070657607314573158634318579034399949163134718214043234989746643128500000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841} and \frac{30948500982134506872478105600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841} to get \frac{159609055344292807849099926888186639629762460783631819674990330449993092747148151712779346455547025504296617968174505933098834575687480070657607314573158634318579034399949163134718214043234989746643128500000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}.

$$\frac{159609055344292807849099926888186639629762460783631819674990330449993092747148151712779346455547025504296617968174505933098834575687480070657607314573158634318579034399949163134718214043234989746643128500000}{162954229757708923674492094241679492260136284764006246986540079041692913158574003657311609463391248167408330035347043087359404274655354552494705104752060758810862089294347841376220887608359099480055849841}$$