Use the compound interest formula A=P(1+r)^t and the given information to solve for r.
A=9,000,000
P=80,000
t=40
I have done this problem over a over and still get the wrong answer.
Is it compounded daily, monthly, quarterly, semi-annually, or annually?
The value of r is meaningless without
the compounding frequency. Also, my Eq
uses n instead of t. n is the # of compounding periods.
A = P(1+r)^t,
Divide both sides by P:
(1+r)^t = A / P,
tLog(1+r) = Log(A/P),
40Log(1+r) = Log(9,000,000/80,000),
40Log(1+r) = Log112.5,
Divide both sides by 40:
Log(1+r) = Log112.5 / 40,
Log(1+r) = 2.0512 / 40,
Log(1+r) = 0.051(1+r),
Exponential form:
(1+r) = 10^(0.0512788),
1+r = 1.1253,
r = 1.1253 - 1 = 0.1253 = 12.53%.
I showed several extra steps; hopefully, you will understand what I did.
To solve for the interest rate (r), we can use the compound interest formula and substitute the given values:
A = P(1 + r)^t
Substituting the given values:
9,000,000 = 80,000(1 + r)^40
First, let's divide both sides of the equation by 80,000 to isolate the term (1 + r)^40:
9,000,000 / 80,000 = (1 + r)^40
This simplifies to:
112.5 = (1 + r)^40
To get rid of the exponent, we can take the 40th root of both sides:
∛(112.5) = ∛((1 + r)^40)
Now, we have:
1 + r = ∛(112.5)
Subtracting 1 from both sides gives:
r = ∛(112.5) - 1
Using a calculator, the cube root (∛) of 112.5 is approximately 4.25.
Therefore, the interest rate (r) is:
r ≈ 4.25 - 1
r ≈ 3.25
So, the interest rate is approximately 3.25.
To solve for the interest rate (r), we can use the formula for compound interest:
A = P(1 + r)^t
In this case, we have the following values:
A = 9,000,000
P = 80,000
t = 40
Substituting these values into the formula, we get:
9,000,000 = 80,000(1 + r)^40
Now, let's simplify this equation step by step to solve for r:
1. Divide both sides of the equation by 80,000 to isolate (1 + r)^40:
9,000,000 / 80,000 = (1 + r)^40
Since 1 + r raised to the power of 40 is on the right side of the equation, let's simplify the left side:
112.5 = (1 + r)^40
2. To isolate (1 + r), we need to take the 40th root of both sides of the equation:
(112.5)^(1/40) = 1 + r
Now we have an equation with (1 + r) on one side and a number on the other side.
3. Evaluate the expression (112.5)^(1/40) using a calculator:
(112.5)^(1/40) ≈ 1.0264
4. Subtract 1 from both sides of the equation:
1.0264 - 1 = r
r ≈ 0.0264
Therefore, the interest rate is approximately 0.0264, which is equivalent to 2.64%.