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Calculate the simple interest and total amount if the principal is P, rate is 8% per year, and time is 5 years.

Mathematics

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Step-by-step solution

4 steps
  1. Identify the formula for simple interest.

    The formula for simple interest (II) is:

    I=Prt100I = \frac{Prt}{100}

    where PP is the principal amount, rr is the annual interest rate, and tt is the time in years.

  2. Identify the given values.

    From the problem statement:

    • Time (tt) = 5 years
    • Annual interest rate (rr) = 8%8\% The principal amount (PP) is not given, so we will express the interest and total amount in terms of PP.
  3. Calculate the simple interest.

    Substitute the given values into the simple interest formula:

    I=P×8×5100I = \frac{P \times 8 \times 5}{100} I=40P100I = \frac{40P}{100} I=0.4PI = 0.4P

    The simple interest earned is 0.4P\boxed{\text{0.4P}}.

  4. Calculate the total amount.

    The total amount (AA) after tt years is the principal plus the interest:

    A=P+IA = P + I A=P+0.4PA = P + 0.4P A=1.4PA = 1.4P

    The total amount is 1.4P\boxed{\text{1.4P}}.

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