Answer:
Explanation:
Interest is a percentage of an original amount that is added to the original amount. The percentage is called the interest rate. It is usually given as an interest rate per year.
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Example 1:
Question: You invest $100 for 1 year at an interest rate of 5% per year. How much is your investment worth after 1 year?
Answer:
The interest earned in 1 year is 5% of $100.
5% of $100 = 0.05 × $100 = $5
The actual amount of the interest earned in 1 year is $5.
Now you add the $5 to the original $100, and at the end of 1 year, you have $105.
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What happens if your money stays invested for more than 1 year? If it is invested with simple interest rate, then the interest you earn for 2 years, or 3 years is just 2 or 3 times the interest you would have earned for 1 year.
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Example 2:
Question: You invest $500 for 3 years at an interest rate of 4% per year. How much is your investment worth after 3 years?
Answer:
The interest earned in 1 year is 4% of $500, so the investment earned in 3 years is 3 × 4% × $500.
3 × 4% of $500 = 3 × 0.04 × $500 = $60
The actual amount of the interest earned in 3 years is $60.
Now you add the $60 to the original $500, and at the end of 3 years, you have $560.
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The formula for simple interest is
I = Prt,
where P = the principal amount, the amount invested
r = annual interest rate usually given as a percent (convert to decimal to use in the formula)
t = number of years
Once you find the amount of interest, I in the formula above, you add that to P, the amount invested, to find the total amount the investment is worth after t years.
The important thing to remember about simple interest is that simple interest is earned only on the principal mount, the amount that was invested.
Compound interest is interest that is earned on the principal and on the accumulated interest.
Let's look again at our examples above, but now we use the simple interest formula to answer the questions.
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Example 1 (using simple interest formula):
Question: You invest $100 for 1 year at an interest rate of 5% per year. How much is your investment worth after 1 year?
Answer:
I = Prt = $100 × 0.05 × 1 = $5
total value = $100 + $5 = $105
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Example 2 (using simple interest formula):
Question: You invest $500 for 3 years at an interest rate of 4% per year. How much is your investment worth after 3 years?
Answer:
I = Prt = $500 × 0.04 × 3 = $60
total value = $500 + $60 = $560
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