Econ 299 Chapter1b - 1.4InterestRates project situations...

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1.4 Interest Rates Interest rates are important in economics,  as they show the opportunity cost of a  project. Different interest rates apply to different  situations. Different interest rates are available to  different people.
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1.4 Interest Rate Examples (Sept 05) Bank of Canada Rate: 2.75% 1 Year GIC: 1.4% 1 Year Cashable GIC: 1.15% 3 Year GIC: 2.05% 3 Year Cashable GIC: 1.8% Bank Account: 0.0% 1 year closed Mortgage: 5% 1 year open Mortgage: 7.35% 1 Year T-bill: 2.78% (1.5% via bank)
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1.4 Interest Rate Rules Bank of Canada rate for banks Is less than Chartered Banks’ rates for best corporate  customers (Prime Rate) Is less than Typical Bank Rate More risk = higher rate
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1.4.2 Real Vrs. Nominal Rates Super Savings Bank Account: 2% interest Cash on hand: $100 2 DVD players:  Basic: $100 DVD Playback Advanced: $102 DVD/VCD/SVCD/AVI/DVD ± R/CD/CD ± R Progressive Scan, Stop Memory, Blue
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1.4.2 Real Vrs. Nominal Rates You want the deluxe, so you invest for a  year, cash on hand in a year: $102 But, due to 3% inflation, the DVD players  now cost: $103 (basic) $105.06 (deluxe) Now you can’t afford either You’ve LOST buying power
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1.4.2.1 Calculating real interest r r real real  = (1+r  = (1+r nom nom ) )                     ---------  -1 ---------  -1         (1+inf) (1+inf) r real = real interest rate r nom = nominal interest rate inf = inflation
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r real  = (1+r nom -1-inf)    ---------------- (1+inf) r real + r real *inf = r nom -inf   (r real *inf is small) r real   = r nom  – inf Last example: r real  = 2%-3%=-1% 1.4.2.1 Easy Interest Formula
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1.4.2.1 Interest Reality Very few short-term investments currently  in Canada offer a return greater than  inflation. While investments are a good way to  transfer money from one period to the  other, they are currently useless for  “making” money. If deciding only between buying now or  later, one should buy now, before one’s  currency falls in real value.
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1.4.2.1 Calculating currency interest You can invest in Canada, the US, or  Mexico.  Investment opportunities are  4%, 5%, and 15% respectively. However, country currency inflation is 2%,  3% and 14% Real interest rate then becomes: Canada: 4%-2%=2% US: 5%-3%=2% Mexico: 15%-14% = 1%
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1.4.3.1 Annual Compounding Investment: $100   Interest rate: 2% Year Calc. Amount 1 100 100.00 2 100*1.02 102.00 3 100*1.02 2 104.04 4 100*1.02 3 106.12 5 100*1.02 4 108.24 Derived Formula: S = P (1+i) t S = value after t years P = principle amount i = interest rate t = years
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1.4.3.2 More Frequent Compounding If interest is compounded m times a year, 1/m  of the interest is paid each time Modified Formula: S = P (1+[i/m]) mt S = value after t years P = principle amount i = interest rate           t = years m = times compounded (monthly = 12, etc) Infinite Compounding:  S = Pe it
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Compounding Comparison  Yearly vrs. biyearly
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