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.
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 |
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