Learning Objectives for Section 3'1 Simple Interest

1
Learning Objectives for Section 3.1 Simple
Interest

• After this lecture, you should be able to
• Compute simple interest using the simple interest
  formula.
• Solve problems involving investments and the
  simple interest formula.

2
Some Preliminary Notes

• We will use 360-days for one year when computing
  time.
• Time must be in terms of years to use in the
  formulas.
• All rates must be converted to decimals to use in
  formulas.
• When an answer is rounded, use the symbol ?
  instead of .
• We will round to the nearest cent for dollar
  amounts, unless otherwise stated.
• Try to avoid rounding until the final answer.

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Conversions Time Periods

• Example 1 Convert the given time periods into
  years
• 180 days b) 120 days c) 3 quarters
• d) 7 months e) 60 days f) 26 weeks

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Conversions Percents to Decimals

• Example 2 Convert the given percents to
  decimals
• 4.5 b) .32 c) 112

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Conversions Decimals to Percents

• Example 3 Convert the given decimals to
  percents
• 0.06 b) 5 c) 0.11

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Simple Interest Formula
Simple Interest Formula where I interest
P principal (amount invested)
r annual simple interest rate (as a
decimal) t time in years
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An Example

• Example 4 Find the interest on a boat loan of
  5,000 at 16 for 8 months.

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Total Amount to Be Paid Back
Example 5 What is the total amount to be paid
back on the boat loan in Example 4?

• The total amount to be paid back for the boat
  loan would be 5000 plus the interest of 533.33,
  for a total of 5,533.33.
• In general, the future value (amount) is given by
  the following equation
• A P I
• A P Prt
• P (1 rt)

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Another Example

• Example 6 Find the total amount due on a loan
  of 600 at 16
• interest at the end of 15 months.

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Another Example

• Example 7 A loan of 10,000 was repaid at the
  end of 6 months.
• What amount (principal and interest) was repaid,
  if a 6.5 annual
• rate of interest was charged?

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Application

• Example 8 A department store charges 18.6
  interest (annual) for overdue accounts. How much
  interest will be owed on a 1,080 account that is
  3 months overdue?

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Interest Rate Earned on a Note

• Example 9 What is the annual interest rate
  earned by a 33-day T-bill with a maturity value
  of 1,000 that sells for 996.16?

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Interest Rate Earned on a NoteSolution

• Solution Use the equation A P (1 rt)
  1,000 996.16

We normally use 360 days for a financial year
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Purchase Price of a Note

• Example 10 What is the purchase price of a
  26-week T-bill with a maturity value of 1,000
  that earns an annual interest rate of 4.903?