Unformatted text preview: ChE 3171, Spring 2010, Week 1 Inflation: Usually defined as an increase in the money supply. Fc,n = Pc (1 + f )n , Fn = P (1 + f )n where: f is inflation rate over 1 period, Pc is present cost, Fc,n is future cost after n periods. P is present purchasing power of an amount of money and Fn is future purchasing power of the same amount of money after n periods. The interest rate, f , is almost always given on a yearly basis. Different commodities may have different inflation rates. Interest: Simple interest is calculated based on the original principal, P0 , only. Pn = Pn-1 + iP0 Pn = P0 + niP0 where i is interest rate over a period, n is number of periods, P0 is initial principal and Pn the principal after n periods. Compound interest is based on the current amount of principal, Pn . Pn = Pn-1 (1 + i) Pn = (1 + i)n P0 where i is interest rate over a period, n is number of periods, P0 is initial principal and Pn the principal after n periods. Interest rates are commonly reported as the nominal annual rate, r, but interest may accrue more frequently. If interest accrues over m periods in a year, then the effective annual rate, ic , is r m -1 m Continuous compounding: When time is measured in years, the principal increases as ic = 1 + P (t) = P (t0 )er(t-t0 ) , i c = er - 1 Time value of money: The anticipated rate of increase of an investment. Annuities: Periodic payments on e.g. a loan or into a fund. Unless stated otherwise, assume annuity payments have the same period as the period over which interest accrues. For annuities that pay down a loan and into a principal, the principal chances as Pay down loan: Pn+1 = Pn (1 + i) - An Pay into principal: Pn+1 = Pn (1 + i) + An where An is the n'th annuity payment and i is the interest over 1 period. Excel: Relative and absolute cell references. Named cells for absolute references, goal seek. 1 ...
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- Spring '10
- Inflation, pn, Initial Principal