Question

A 20-year loan requires semi-annual payments of $1,333.28 including interest at 10.75% compounded semi-annually. What is the original amount of the loan and what will be the balance of the loan 8 ½ years later (just after the scheduled payment)?

*Require formulas/written out and not spreadsheet. Thank you.

Answer 1

1]	Original amount of the loan is the PV of the semi-annual installments discounted at 10.75%/2 per half year
	=1333.28*((1+0.1075/2)^40-1)/((0.1075/2)*(1+0.1075/2)^40) =	$               21,750
2]	Balance of loan after 8 and a half years [after 17 semi-annual
	installments] = PV of 23 remaining installments =
	=1333.28*((1+0.1075/2)^23-1)/((0.1075/2)*(1+0.1075/2)^23) =	$               17,365