Suppose that you took a mortgage of 100000 on a house to be paid back in full by 10 equal annual installments, each consisting of the interest due on the outstanding balance plus a repayment of a part of the amount borrowed. If you decided to clear the mortgage after eight years, how much money would you need to pay on top of the eight installment, assuming that a constant annual compounding rate of 6% applies throughout the period of the mortgage?
I know how to find the payment amount if we had to pay the mortgage back in 10 years: $C=\frac{100,000}{PA(6\%, 10)} = 13,586.80$ where C= payment amount, PA= present value of annuity and $PA(n, r)= \frac{1-(1+r)^{-n}}{r}$
But I am confused on how to figure how much money I need to pay on top of the eigth installment if I decide to clear the mortgage after eight years instead of ten?
My textbook says to do $PA(6\%, 2) \times 13,586.8 = 24,909.93$ but I don't understand why this is correct?