Find the amount of time.
I = $10, P = $100, r = 2%
Group of answer choices
2. Find the annual interest rate.
I = $40, P = $500, t = 16 months :)
Just plug your numbers into
I = Prt
and solve for the missing amount
To find the amount of time, we can use the formula for simple interest:
I = P * r * t
where:
I = interest earned
P = principal amount (initial investment)
r = interest rate (expressed as a decimal)
t = time (in years)
Given:
I = $10
P = $100
r = 2%
Substituting the values into the formula, we have:
$10 = $100 * 0.02 * t
To find t, we can rearrange the equation:
t = $10 / ($100 * 0.02)
Simplifying, we get:
t = $10 / $2
t = 5 years
Therefore, the amount of time is 5 years.
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To find the annual interest rate, we can use a similar formula:
I = P * r * t
Given:
I = $40
P = $500
t = 16 months
However, since the time is given in months, we need to convert it to years by dividing it by 12:
t = 16 months / 12 = 4/3 years
Substituting the values into the formula, we have:
$40 = $500 * r * (4/3)
To find r, we can rearrange the equation:
r = $40 / ($500 * (4/3))
Simplifying, we get:
r = $40 / ($500 * 4/3)
r = $40 * (3/4) / $500
r = $120 / $2000
r = 0.06
To express the interest rate as a percentage, we multiply it by 100:
r = 0.06 * 100
r = 6%
Therefore, the annual interest rate is 6%.
To find the amount of time in the first scenario, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest earned
P = Principal amount
r = Annual interest rate
t = Time in years
In the given scenario, we have:
I = $10
P = $100
r = 2%
We need to find the value of t.
Rearranging the formula, we can solve for t:
t = I / (P * r)
Substituting the given values:
t = $10 / ($100 * 0.02)
Simplifying the expression:
t = $10 / $2
t = 5 years
So, the amount of time in this scenario is 5 years.
Now, let's move on to the second scenario - finding the annual interest rate.
Again, we'll use the formula for simple interest:
I = P * r * t
In this case, we're given:
I = $40
P = $500
t = 16 months
First, we need to convert the time to years. Since we have the time in months, we divide it by 12:
t = 16 months / 12
t = 1.33 years
Now, substituting the given values into the formula:
$40 = $500 * r * 1.33
Rearranging the formula to solve for r:
r = I / (P * t)
Substituting the given values:
r = $40 / ($500 * 1.33)
Simplifying the expression:
r = $40 / $665
r ≈ 0.0602
Converting this to a percentage:
r ≈ 6.02%
So, the annual interest rate in this scenario is approximately 6.02%.