Solve PMT=15,000(0.063/12)/1-(1+frac{0.063{12})^-12(3)}

$$PMT = \frac { 15,000 ( \frac { 0.063 } { 12 } ) } { 1 - ( 1 + \frac { 0.063 } { 12 } ) ^ { - 12 ( 3 ) } }$$

Solve for M

$$M=\frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268PT}$$

$$T\neq 0\text{ and }P\neq 0$$

Steps for Solving Linear Equation

Expand \frac{0.063}{12} by multiplying both numerator and the denominator by 1000.

$$PMT=\frac{15000\times \frac{63}{12000}}{1-\left(1+\frac{0.063}{12}\right)^{-12\times 3}}$$

Reduce the fraction \frac{63}{12000} to lowest terms by extracting and canceling out 3.

$$PMT=\frac{15000\times \frac{21}{4000}}{1-\left(1+\frac{0.063}{12}\right)^{-12\times 3}}$$

Multiply 15000 and \frac{21}{4000} to get \frac{315}{4}.

$$PMT=\frac{\frac{315}{4}}{1-\left(1+\frac{0.063}{12}\right)^{-12\times 3}}$$

Expand \frac{0.063}{12} by multiplying both numerator and the denominator by 1000.

$$PMT=\frac{\frac{315}{4}}{1-\left(1+\frac{63}{12000}\right)^{-12\times 3}}$$

Reduce the fraction \frac{63}{12000} to lowest terms by extracting and canceling out 3.

$$PMT=\frac{\frac{315}{4}}{1-\left(1+\frac{21}{4000}\right)^{-12\times 3}}$$

Add 1 and \frac{21}{4000} to get \frac{4021}{4000}.

$$PMT=\frac{\frac{315}{4}}{1-\left(\frac{4021}{4000}\right)^{-12\times 3}}$$

Multiply -12 and 3 to get -36.

$$PMT=\frac{\frac{315}{4}}{1-\left(\frac{4021}{4000}\right)^{-36}}$$

Calculate \frac{4021}{4000} to the power of -36 and get \frac{4722366482869645213696000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}.

$$PMT=\frac{\frac{315}{4}}{1-\frac{4722366482869645213696000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}}$$

Subtract \frac{4722366482869645213696000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721} from 1 to get \frac{979625885461721207717803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}.

$$PMT=\frac{\frac{315}{4}}{\frac{979625885461721207717803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}}$$

Divide \frac{315}{4} by \frac{979625885461721207717803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721} by multiplying \frac{315}{4} by the reciprocal of \frac{979625885461721207717803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}.

$$PMT=\frac{315}{4}\times \frac{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}{979625885461721207717803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}$$

Multiply \frac{315}{4} and \frac{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}{979625885461721207717803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721} to get \frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268}.

$$PMT=\frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268}$$

The equation is in standard form.

$$PTM=\frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268}$$

Divide both sides by PT.

$$\frac{PTM}{PT}=\frac{\frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268}}{PT}$$

Dividing by PT undoes the multiplication by PT.

$$M=\frac{\frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268}}{PT}$$

Divide \frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268} by PT.

$$M=\frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268PT}$$

Solve for P

$$P=\frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268MT}$$

$$T\neq 0\text{ and }M\neq 0$$

Steps for Solving Linear Equation

Expand \frac{0.063}{12} by multiplying both numerator and the denominator by 1000.

$$PMT=\frac{15000\times \frac{63}{12000}}{1-\left(1+\frac{0.063}{12}\right)^{-12\times 3}}$$

Reduce the fraction \frac{63}{12000} to lowest terms by extracting and canceling out 3.

$$PMT=\frac{15000\times \frac{21}{4000}}{1-\left(1+\frac{0.063}{12}\right)^{-12\times 3}}$$

Multiply 15000 and \frac{21}{4000} to get \frac{315}{4}.

$$PMT=\frac{\frac{315}{4}}{1-\left(1+\frac{0.063}{12}\right)^{-12\times 3}}$$

Expand \frac{0.063}{12} by multiplying both numerator and the denominator by 1000.

$$PMT=\frac{\frac{315}{4}}{1-\left(1+\frac{63}{12000}\right)^{-12\times 3}}$$

Reduce the fraction \frac{63}{12000} to lowest terms by extracting and canceling out 3.

$$PMT=\frac{\frac{315}{4}}{1-\left(1+\frac{21}{4000}\right)^{-12\times 3}}$$

Add 1 and \frac{21}{4000} to get \frac{4021}{4000}.

$$PMT=\frac{\frac{315}{4}}{1-\left(\frac{4021}{4000}\right)^{-12\times 3}}$$

Multiply -12 and 3 to get -36.

$$PMT=\frac{\frac{315}{4}}{1-\left(\frac{4021}{4000}\right)^{-36}}$$

Calculate \frac{4021}{4000} to the power of -36 and get \frac{4722366482869645213696000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}.

$$PMT=\frac{\frac{315}{4}}{1-\frac{4722366482869645213696000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}}$$

Subtract \frac{4722366482869645213696000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721} from 1 to get \frac{979625885461721207717803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}.

$$PMT=\frac{\frac{315}{4}}{\frac{979625885461721207717803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}}$$

Divide \frac{315}{4} by \frac{979625885461721207717803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721} by multiplying \frac{315}{4} by the reciprocal of \frac{979625885461721207717803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}.

$$PMT=\frac{315}{4}\times \frac{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}{979625885461721207717803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}$$

Multiply \frac{315}{4} and \frac{5701992368331366421413803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721}{979625885461721207717803158180847644800353306179453252199134563959311737647314468936448719654761913466340583072498332479637516721} to get \frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268}.

$$PMT=\frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268}$$

The equation is in standard form.

$$MTP=\frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268}$$

Divide both sides by MT.

$$\frac{MTP}{MT}=\frac{\frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268}}{MT}$$

Dividing by MT undoes the multiplication by MT.

$$P=\frac{\frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268}}{MT}$$

Divide \frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268} by MT.

$$P=\frac{28509961841656832107069015790904238224001766530897266260995672819796558688236572344682243598273809567331702915362491662398187583605}{62198468918204521124939883059101437765101797217743063631691083425988046834750125011838013946334089743894640195079259205056350268MT}$$