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Unformatted text preview: MGNT 3125 Fall 2010 Dr. Amine Khayati Chapter 5 Notes I- Future Value and Compounding: 1- Simple interest : Interest earned only on the original principal amount invested; that is, the interest received each year does not earn interest during any subsequent year. * Suppose you invest $1,000 for 2 years at a 5% interest rate per year using simple interest .- At the end of year 1, you earn: 1,000 0.05 = 50- At the end of year 2, you earn: 1,000 0.05 = 50- At the end of year 2, your total value = 1,000 + 50 + 50 = 1,100- Future value (FV) : is the amount of money an investment will grow to over some period of time at some given interest rate. In the earlier example the future value is 1,100. 2- Compound interest : Interest earned on both the initial principal and the interest reinvested from prior periods. * Suppose you invest $1,000 for 2 years at a 5% interest rate per year using compound interest .- At the end of year 1, you earn: 1,000 0.05 = 50- You reinvest the $50 interest you earned in year 1- At the end of year 2, you earn: 1,000 0.05 = 50 And 50 0.05 = 2.5- At the end of year 2, your total value = 1,000 + 50 + 50 + 2.5 = 1,102.5 The $2.5 comes from the interest you earned in year 2 from reinvesting the interest you earned in year 1.- The process of leaving your money and any accumulated interest in an investment and thereby reinvesting the interest is called compounding . It also means earning interest on interest. The future value at year 1 = 1,000 (1.05) = 1,050 The future value at year 2 = 1,000 (1.05) (1.05) = 1,102.5 = 1,000 (1.05) = 1,102.5 The General formula for Future Value (FV): Where: FV: future value 1 PV: present value r: period interest rate, expressed as decimal t : number of periods * Suppose you invest the $1,000 from the previous example for 5 years, how much would you have using the simple interest and using compound interest? Determine the effect of compounding.- Simple interest: 1,000 + (1,000 0.05 5) = 1,250- Compound interest: 1,000 (1.05) = 1,276.28- The effect of compounding = 1,250 – 1,276.28 = 26.28 Compounding added 26.28 to the value of the investment. Repeat the same example for an investment period of 10 years:- Simple interest: 1,000 + (1,000 0.05 10) = 1,500- Compound interest: 1,000 (1.05) = 1,628.89- The effect of compounding = 1,500 – 1,628.89= 128.89 Compounding added 128.89 to the value of the investment. The effect of compounding increases as the number of periods increases. II- Present Value and Discounting:- The present value (PV) is the amount of money that you need to invest today at certain interest rate in order to reach some amount in the future (future value)....
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