How many monthly payments remain to be paid on an 8% mortgage with a 30-year amortization and monthly payments of $733.76, when the balance reaches one-half of the $100,000 mortgage?

 Approximately 91 payments

Explanation:

Target Balance = PV = $100,000 x 1/2 = $50,000

R = Pi ( 1- ( 1 + i )-n

733.76 = 50,000 x 0.0067 / ( 1 - ( 1 + 0.0067 )-n

733.76 = 335 / ( 1 - ( 1 + 0.0067 )^-n

1 - ( 1 + 0.0067 )^-n = 335 / 733.76

1 - ( 1 + 0.0067 )^-n = 0.45655

(1 + 0.0067 )^-n = 0.45655 - 1

-(1 + 0.0067 )^-n = -0.54345

(1 + 0.0067 )^-n = 0.54345

(1.0067 )^n = 1 / 0.54345

(1.0067 )^n = 1.84010

n log 1.0067 = log 1.84010

n = log 1.84010 / log 1.0067

n = 94.322 = 91 (approximately)

$2.00 for three shots.

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