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Sec 5.3 Compound Interest Compound Interest Formula r mt A = P (1 + ) m where A = Accumulated amount at the end of t years. P = Principal r = Nominal interest rate per year m = Number of conversion periods per year t = Term (number of years) Present Value Formula for Compound Interest r −mt P = A(1 + ) m Continuous Compound Interest Formula A = P ert where P = Principal r = Annual interest rate compounded continuously t = Time in years A = Accumulated amount at the end of t years Present Value Formula for Continuous Compound Interest P = Ae−rt Example 1 Find the accumulated amount A if the principal P=$2500, interest rate r=7%, after t=10 years, and compounded semiannually. Solution. Compounding semiannually means that m=2, r mt 0.07 (2)(7) A = P (1 + ) = 2500(1 + ) = 2500(1.035)14 = 4046.7 m 2 1 Example 2 Find the interest rate needed for an investment of $5000 to grow to an amount of $7500 in 3 yr if interest is compounded monthly. Solution. Here P=5000, A=7500, t=3, m=12, from the formula r (3)(12) 7500 = 5000(1 + ) 12 Solve this equation, r 3 36 ln(1 + ) = ln 12 2 then r ln 3 2 1+ = e 36 12 then ln 3 2 r = 12(1 − e 36 )= Example 3 Find the interest rate needed for an investment of $4000 to double in 5 yr if interest is compounded continuously. Here P=4000, A=(2)(4000)=8000, t=5, from the formula 8000 = 4000e5r Then 5r = ln 2 then ln 2 r= 5 Example 4 How long will it take an investment of $8000 to double if the investment earns interest at the rate of 8% compounded continuously? Solution. Here A=(2)(8000)=16000, and P=8000, and r=0.08, from the formula 16000 = 8000e0.08t then ln 2 t= 0.08 In real application, we have options to choose the best strategy. There- fore, we have to compare the results from diﬀerent plans or diﬀerent formula. Either we want the shortest time or the largest accumulated compound. 2

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posted: | 8/11/2008 |

language: | English |

pages: | 2 |

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This is an example of compound interest formula. This document is useful for conducting compound interest formula.

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