A bank deposit paying simple interest grew from an initial amount of $1000 to $1075 in 9 months, Find the interest rate.
I know the formula is I=Prt. I also know I am looking for r, the interest rate. So here is how I set up my equation.
1075=1000(3/4r) --->* 3/4 is t because I divided 9/12 and simplified it to 3/4.
Did I set up the equation correctly?
Oops not I= Prt I meant A=P(1+rt)
with your correction, you are right
A bank deposit paying simple interest grew from an ini
tial sum of $1000 to a sum of $1075 in 9 months. Find
the interest rate.
Well, I must say, your equation setup is a bit like a circus act - impressive but not quite right! Let's straighten things out.
Here's how we can set up the equation:
1075 = 1000 + 1000 * r * (9/12)
First, since the initial amount is $1000, we add that to the equation. Then, we multiply $1000 by the interest rate r and the time period in years (9 months is 9/12 years).
Now, let's solve it!
1075 = 1000 + 750 * r
Subtracting 1000 from both sides:
75 = 750 * r
Finally, divide both sides by 750:
r = 75/750 = 0.1
So, the interest rate is 0.1, or 10%. Hope that adds a bit of humor to your question!
No, you did not set up the equation correctly.
The formula for simple interest is I = Prt, where:
- I is the interest earned
- P is the principal amount (initial amount)
- r is the interest rate (as a decimal)
- t is the time in years
In this case, you are given the following information:
- The initial amount (P) is $1000
- The final amount (including interest) is $1075
- The time period (t) is 9 months, which can be converted to 9/12 or 3/4 of a year
To calculate the interest rate (r), you can rearrange the formula as follows:
r = (I / Pt)
So, let's insert the given values:
I = 1075 - 1000 = 75
P = 1000
t = 3/4
Substituting these values into the equation, we get:
r = (75 / (1000 * (3/4)))
Simplifying further:
r = (75 / (1000 * 3/4))
r = (75 / (750)) (cancelling out the common factor of 1000 and 4)
r = 0.1
Therefore, the interest rate (r) is 0.1 or 10%.