Simple interest grew from the initial amount $1000 to $1075 in 9 months. Find the interest rate.
Like always, I will explain my thinking:
I know I have the find r (the interest rate). A=1075 P=1000 t=3/4 (9/12 becomes 3/4)
The formula is A= P(1+rt)
which is then rearranged as r=a-p/pt
r=1075-1000/p(3/4)
r=75/p(3/4)= 75*4/3p
300/3= 100
r=100
To find the interest rate, you correctly identified the formula for simple interest, which is:
A = P(1 + rt)
where A is the final amount, P is the initial principal, r is the interest rate, and t is the time in years.
In this case, you have A = $1075, P = $1000, and t = 9 months (which needs to be converted to years by dividing by 12). Plugging in these values, the equation becomes:
1075 = 1000(1 + r * 9/12)
Simplifying this equation, we have:
1075 = 1000(1 + 3r/4)
Dividing both sides of the equation by 1000 gives:
1.075 = 1 + 3r/4
Subtracting 1 from both sides, we have:
0.075 = 3r/4
To isolate r on one side, multiply both sides of the equation by 4/3:
0.075 * 4/3 = 3r/4 * 4/3
0.1 = r
So, the interest rate is 0.1 or 10%.