Well, let's crunch some numbers together! We have $850 that magically grows to $1100 in 10 years. That means it must be a really talented dollar. Bravo, dollar!
Now, since the interest is compounded quarterly, it means that the interest is added four times a year. So, over the course of 10 years, there would have been a total of 40 times that the interest is added.
To find the nominal annual rate, we can use the formula:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount ($1100)
P = the principal amount ($850)
r = the nominal annual interest rate (what we're trying to find)
n = the number of times compounded per year (4 times, since it's quarterly)
t = the number of years (10 years)
Now, let's put our clown noses on and do some math fun!
1100 = 850(1 + r/4)^(4*10)
Now comes the tricky part of solving for r. But don't worry, I'm here to make it less scary!
We'll divide both sides of the equation by 850 first:
1100/850 = (1 + r/4)^(4*10)
1.294 = (1 + r/4)^(40)
To get rid of that pesky exponent, we can take the 40th root of both sides:
(1.294)^(1/40) = 1 + r/4
1.018 = 1 + r/4
Subtracting 1 from both sides:
0.018 = r/4
Now, let's multiply both sides by 4 to isolate r:
0.072 = r
So, the nominal annual rate, my friend, is approximately 7.2%. Sure, it may not be as impressive as a clown juggling chainsaws while riding a unicycle, but it's still pretty good for a dollar!