MATH 2FM3 Lecture 15: Lect15

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3. 2 amortization of loan repayment with level payments: so far we had arbitrary payments k1, k2, , kn. Now we consider the easier case with constant level payments of k: suppose a loan l is taken at time 0 and is to be repaid with level payments of amounts. K at times 1, 2, , n. if the interest rate per period is i, the equation value at time 0 for this loan is. L an(cid:101)i since the loan must equal the present value of all payments: let us assume for simplicity that k = 1 so l = ob0 = an(cid:101)i. Obt = l(1 + i)t (1 + i)t 1 (1 + i)t 2 1 = an(cid:101)i (1 + i)t st(cid:101)i. The total amount paid for the loan is kt = n and the total interest paid is (cid:18) 1 n. = (1 n) + (1 n 1) + + (1 ) = n an(cid:101)i.