Paul Meyer Lesson Plan For HMA194

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Lecture 8

Compound Interest Formula [math]S=P(1+i)[/math]n

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  • We are going to calculate the following
  1. The present value P given the future value S , interest rate i and duration n
  2. The interest rate i given S, P and n
  3. The length or duration of an investment given S, P and i
  • Perform the following funtions on your calculator
  1. Natural logarithm function ln
  2. Exponential function e
  • Differentiate between Compound interest and Simple interest

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  • Use your calculator to perform
  1. Power calculations
  2. Using brackets for calculations
  3. Use fraction key on your calculator
  • How to substitute values into formulae
  • How to transpose formulae

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  1. Given the compound interest formulae [math]S=P(1+i)[/math]n, transpose the equation to make P the subject.
    • To get [math]P=S/(1+i)[/math]n
    • Use your tranposed equation to calculate the following
    1. Sina is hoping to by a piece of land in 6 years time for $100,000.00. How much should she invest now if the bank offers an interest rate of 9.5%p.a. compounded annually?
    2. Sione's investment has matured after 10 years at 12% p.a. compounded monthly. How much did he invest if his investment earned $15,000 interest?
  2. Locate the natural logarithmic key on your calculator (nb most models it will be the "ln" key)
    • Calulate ln .0214
    • Calulate ln 5.6
  3. Transpose the CI formulae to make n the subject.
    • To get [math]n=ln(S/P)/ln(1+i)[/math]
    • Use your transposed formulae to calculate the following
    1. How long will it take for an investment to double given an interest rate of 9.5% p.a. compounded quarterly?
    2. An investment of $15,000 has a future value of $21,000 at an interest rate of 6%p.a. compounded annually. How long did it take the investment to mature?
  4. Locate the exponential key on your calculator (e)
    • it is usually the same key as the natural logarithm but you need to access it by pressing shift first
    • Calculate
    1. e5.0345
    2. e-1.23
  5. Transpose the CI formulae to make i the subject.
    • To get [math]i=e[/math]ln(S/P)/n- 1
    • Use the transposed equation to calculate
    1. Sui has $75,000 she wishes to buy some land in 4 years time which is worth $95,000. At what interest rate must she invest her money if it is compounded annually?
    2. Tiana wants to find the interest rate that will triple her investment in 6 years time compounded quarterly?

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At the end of todays lesson you should be able to

  1. Use calculators to calculate natural logarithms and exponentials
  2. Substitue values correctly into any of the four forms of the CI formulae
  3. Calculate S,P,i and n given the other three values
  4. Identify the difference between Compound interest and Simple interest (last weeks lesson)

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Do exercise 8 from our reader