02_Time_Value_of_Money-Day_1

# The market interest rate is 8 what is the pv fv pv1rt

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The market interest rate is 8%. What is the PV? FV = PV×(1+r×t) PV= FV / (1+r×t) PV = 200 / (1+0.08×5) = \$142.86

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Ex. 7: r & t with Simple Interest Carol put \$40 in the bank 4 years ago. Now she has \$50. What r did she earn in simple interest? FV = PV×(1+r×t) r = (FV/PV-1) / t r = (FV/PV-1) / t = (50/40 - 1) / 4 = 0.0625 = 6.25% Dan put \$300 in an account earning 13% simple interest per year. Now he has \$400. How many years was his money invested? FV = PV×(1+r×t) t = (FV/PV-1) / r t = (FV/PV-1) / r = (400/300-1) / 0.13 = 2.56 years
Ex. 8: Simple & Compound Interest Edward invested \$100 for 8 years in an account paying 7% simple interest. Fay invested \$100 for 8 years in an account paying 5.8% compound interest. Which is worth more after 8 years? Edward gets simple interest: FV t = PV×(1+r×t) FV 8 = 100×(1+0.07×8) = \$156 Fay gets compound interest: FV t = PV×(1+r) t FV 8 = 100×(1+0.058) 8 = \$156.99 Fay's investment is worth more (\$156.99 > \$156).

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Lecture Problems Eric invested \$500 in an account that earns 8% simple interest per year. How much will he have in 15 years? Jane can earn 7% per year in compound interest. How much would Jane need to invest today to have as much as Eric in 15 years? If Martha invests \$500 in an account that earns 9% per year in compound interest, how much will she have in 12 years? If Carl can invest \$600 today, then what rate of simple interest would Carl need to earn each year to have as much as Martha in 12 years?
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