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Interpret principal, interest rate, and time

Principal is the initial amount invested or borrowed, the interest rate is the percentage of that principal earned or charged per time period, and time is the number of matching periods; these quantities determine simple interest through I=PrtI=Prt and the resulting balance through A=P+IA=P+I. The interpretation distinguishes interest from total amount and requires rates to be expressed consistently with the time unit; compound interest, changing rates, and other advanced cases are not included.

Detailed Explanation: Interpret principal, interest rate, and time

In a simple-interest problem, identify three quantities:

  • Principal (PP): the starting amount invested or borrowed.
  • Interest rate (rr): the percent earned or charged during each time period. Write it as a decimal.
  • Time (tt): the number of time periods. The time unit must match the rate’s unit.

Use the formulas

I=PrtI=Prt

to find the interest, and

A=P+IA=P+I

to find the total amount, or balance.

Example: You invest 600atanannualinterestrateofat an annual interest rate of5%forfor3$ years. How much interest do you earn, and what is the final balance?

Step 1: Identify the quantities.

  • P=600P=600
  • r=5%=0.05r=5\%=0.05
  • t=3t=3 years

The rate is annual, and the time is given in years, so the units match.

Step 2: Find the interest.

I=PrtI=Prt I=(600)(0.05)(3)=90I=(600)(0.05)(3)=90

You earn 90$ in interest.

Step 3: Find the total amount.

A=P+IA=P+I A=600+90=690A=600+90=690

The final balance is 690}.The. The $90istheinterest,whiletheis the interest, while the$690$ is the total amount including the original principal.

Learn by doing: Interpret principal, interest rate, and time

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    Interest (Simple) - Interest from Principle, Rate, and Time

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