ECON222 WEEK2 Finance-3

ECON222 WEEK2 Finance-3 - A is the present value of the...

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1 1 Lecture 5: Topic: Mathematics of Finance Reading for this lecture Homework for Tutorial in Week 3 Ex 5.5, pp. 221-222, problems 1, 5, 19. 2 A Loan A loan of $A at a given interest rate, r, is to be repaid in a sequence installments of the same size, R, at fixed intervals of time over the term of the loan, n. • Find A, given R, r and n. • Find R, given A, r and n. • How much of R is principal; how much is interest? 3 Loan Repayments Annuity Period 1 2 …. n-1 n . | | | | | | R R R R R R R R Loan, A A = R(1+r) -1 + R(1+r) -2 + …. + R(1+r) -n A= R[1 – (1+r) -n ] r R= rA [1 – (1+r) -n ] formula for PV of an ordinary annuity 4 Car Loan Example Jack wants to purchase a new car and can afford repayments of $200 per month. His bank will give him a 5 year loan at 6% compounded monthly. Jack is able to pay a $1,000 down payment from his savings. How expensive a car can Jack afford (to the nearest dollar)? 5 Car Loan
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Unformatted text preview: A is the present value of the loan, R = r = n = A = R[1 – (1+r)-n ] r The most expensive car that Jack can afford is (to the nearest dollar). 6 Amortization of Loans The loan outstanding at the end of a given period = The loan outstanding at the beginning of the period minus the amount of principal that was repaid during the period. • Interest paid for the period = (r)(loan outstanding at the beginning of the period) • Principal repaid = R - Interest paid for the period 2 7 Amortization of Loans Ex 5.5, pp. 221-222, problem 7 Construct an amortization schedule for a loan of $5,000 repaid by 4 equal yearly repayments with interest at 7% compounded annually. First find the repayment, R, per year. A = r = n = 4 R = rA [1 – (1+r)-n ] 8 Amortization Schedule Principal Interest Payment Principal Outst’g paid for repaid (beginning) period 1 2 3 4 Total...
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This note was uploaded on 06/16/2010 for the course ECON 220 taught by Professor Drea during the Spring '10 term at Uni. West.

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ECON222 WEEK2 Finance-3 - A is the present value of the...

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