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09_Lecture_Econ_basics

# 09_Lecture_Econ_basics - Managerial Economics BEE 489...

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1 Managerial Economics BEE 489 Entrepreneurship Time Value of Money

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2 Economic Terms to Memorize r = Interest rate per interest period w/out compounding i = Interest (effective, APR) rate per interest period. n = Number of interest periods. m = Number of compounding subperiods per period P = A present sum of money. F = A future sum of money. The future sum F is an amount, n interest periods from the present, that is equivalent to P with interest rate i. A = An end-of-period cash receipt or disbursement in a uniform series continuing for n periods, the entire series equivalent to P or F at interest rate i.
3 Interest Rates--recap r = interest rate without considering compounding, sometimes called “nominal” interest i = effective interest rate per defined interest rate period i a = effective interest rate per annum, sometimes called APR

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4 Simple Interest E = P * r * n Examples: If you borrow \$100 for one year at 10% per annum (period), E = (\$100)(0.10)(1) = \$10 If you borrow \$100 for 3 months at 10% E = (\$100)(0.10)(3/12) = \$2.50 P = principal borrowed r= interest rate per annum n= number of periods
5 Compound Interest E = P * ( 1 + r ) n - P Examples: If you borrow \$100 for one year at 10% per annum, E= (\$100)(1.10) 1 -100 = \$10 If you borrow \$100 for 3 years at 10% per annum E = (\$100)(1.10) 3 -100 = \$33.1

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6 Nominal vs. Effective Interest Nominal interest rate (r) – the interest rate w/o considering the effect of any compounding. Effective interest rate (APR) – the interest rate taking into account the effect of the compounding.
7 From nominal to effective rate i eff = effective annual interest rate or APR i nom = nominal annual interest rate (r) c = number of compounding periods per year NOTE: i nom /c is sometimes just shown as “i”, i.e. referring to a single interest rate for a single compounding period. 1 1 - + = c nom eff c i i

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8 Example: Nominal to Effective Interest Rate If annual or nominal interest rate is 12% but compounded monthly, then the annual effective interest rate (APR) of 12% compounded each month over 12 months is: % 68 . 12 1 % 100 1268 . 0 00 . 1 12 12 . 0 1 12 = = - + = APR
9 Infinite Series When the number of periods is not specified and an  infinite number of periods is assumed. After  manipulation, the equation for P/A becomes: i A P = Similarly, for the geometric gradient: i G i G P 2 = = Pi i G A A Pi = = and

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