ECON222 WEEK1 Finance-1

# ECON222 WEEK1 Finance-1 - Lecture 3 Topic Mathematics of...

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1 1 Lecture 3: Topic: Mathematics of Finance Reading H&P, Ch 5. Reading for this lecture H&P, Ch 5, Sect 5.1 - 5.2; (also refer back to Ch 4, pp. 167-168) Homework for Tutorial in Week 2 Ex 5.1, pp. 200-201, problems 1, 3, 9, 11. Ex 5.2, pp. 204-205, problems 3, 11, 15, 19. 2 Compound Interest Suppose \$100 is invested at 8 percent per annum. Interest is earned and reinvested at the end of every quarter. What is the compound amount after 1 year? Principal = \$100 Nominal interest rate = 8% per year Quarterly interest rate = 8/4 = 2% per quarter Number of quarters = 4 3 Compound Interest End of Qtr 1: S = 100(1 + 0.02) = 102 End of Qtr 2: S = 102(1 + 0.02) = 104.04 = 100(1 + 0.02)(1 + 0.02) = 100(1 + 0.02) 2 = 104.04 End of Qtr 3: S = 104.04(1 + 0.02) = 106.12 = 100(1 + 0.02) 2 (1 + 0.02) = 100(1 + 0.02) 3 = 106.12 End of Qtr 4: S = 106.12(1 + 0.02) = 108.24 = 100(1 + 0.02) 3 (1 + 0.02) = 100(1 + 0.02) 4 = 108.24 4 Compound Interest Formula S = P(1 + r) n ( formulae for ‘cheat sheet’) where P is the original principal n is the number of conversion periods r is the rate of interest per conversion period S is the compound amount after n periods S – P is amount the compound interest earned 5 Find S , given P, r and n Suppose \$1,000 is invested at 5%. What is the compound amount after 4 years if interest is accumulated (a) annually, (b) semi-annually?

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ECON222 WEEK1 Finance-1 - Lecture 3 Topic Mathematics of...

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