Topic Two - Financial Mathematics

# Topic Two - Financial Mathematics - Topic Two A Review of...

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BUSINESS SCHOOL Topic Two: A Review of Financial Mathematics Craig Mellare

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This Lecture By the end of this lecture you should be able to: - Calculate accumulated cash positions - Value assets with different cashflows - Understand different types of interest rates - Be able to adjust compound interest rates for different time periods - Understand annuities and their valuation - Understand how to use Present and Future Value Tables
Aim of Financial Mathematics Reduce a series of cashflows (asset) to a common \$ base taking into account the time value of money for deciding: - which assets are more value able - appropriate price to pay for assets

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Time Value of Money Which one of these assets would you rather own? Asset 1 Year 0 1 2 3 4 5 6 7 8 |_____|_____|_____|_____|_____|_____|_____|_____| \$100 Asset 2 Year 0 1 2 3 4 5 6 7 8 |_____|_____|_____|_____|_____|_____|_____|_____| \$100
Simple Interest definition - under simple interest, the amount of interest paid per period does not vary and is based on initial cash flow (principal or PV) - FV = PV + \$Interest - but \$Interest = PV x r - hence - FV = PV + (PV x r) FV = PV (1+r) FV = PV (1+r)

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Example A credit union pays 5% p.a. simple interest; you deposit \$1,000; what will be in the account in 4 years? FV = PV (1+r) FV = PV (1+r) FV = 1,000 x (1 + 0.20) = \$1,200 FV = 1,000 x (1 + 0.20) = \$1,200
Compound Interest definition - compound interest arrangements allow for interest to be received during each set period (compounding period), and interest to be earned on the principal plus the interest - key: interest earned on interest FV = PV (1+r) n r = interest rate per period n = number of periods

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Example A credit union pays 5% p.a. compounded yearly, you deposit \$1,000, what will be in the account in 4 years? - FV = PV (1+r) n - FV = 1,000 (1+0.05) 4 = 1,216
What happens if we are borrowing money? Option A - 5% pa compound interest for 5 years? Option B - 5.6% pa simple interest for 5 years? Q: What is the effective simple interest on Option A?

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Effective Simple Interest Rate definition - annual simple interest rate equivalent (ie. effective rate) to a given compound interest rate Over one year: (1+effective rate) = (1 + compound rate m ) m Other than one year: (1+effective rate) = (1 + compound rate m ) mn
Example A credit union offers you a 5 year loan at 5% pa compounded annually. What is the equivalent simple interest on the compound interest loan? effective rate = (1 + compound rate m ) mn -1 effective rate = (1+0.05) 5 - 1 = 28% over 5 years or 5.6% p.a.

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Now do you know which you would prefer? 5% pa compound interest for 5 years?
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Topic Two - Financial Mathematics - Topic Two A Review of...

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