A stuffed animal dealer tells you that a fish he bought for $8 four years ago is now worth $200 follow the steps below to find the effective yield for this investment.
Begin with the equation 8(1+r) ^4=200.Solve for (1+r) ^4
Take the common logarithm of each side of the equation.
Use the power property of Logarithms to rewrite log (1+r) ^4
Solve the equation for log (1+r)
Use exponential logarithmic inverse property to eliminate the logarithm
(Hint: Remember that these are common logarithms) Then solve for R.
If the current trend continues, how much will a $1000 investment in stuffed fish be worth in 3 years?
and how long will it be until you can buy a $1800 computer
8(1+r)^4=200 , divide both sides by 8
(1+r)^4=25
take the fourth root of both sides, no logs needed
1 + r = 25^(1/4) = 2.23606...
r = 1.2306..
the effective rate is appr 123%
so after 3 years, a $1000 investment will be worth
1000(1 + 1.2306067..)^3
= 1000(2.2306067..)^3
= .....
for the last part:
1800 = 1000(2.2306067..)^t
you will need logs for this one
What do you do for the last part
From the instructions to the question, I was assuming
you are studying logarithms
You MUST be able to do a simple equation like this:
1800 = 1000(2.2306067..)^t
hint: divide both sides by 1000, then take log of both sides.
I assume you have a scientific calculator.
To find the effective yield for this investment, follow these steps:
1. Begin with the equation: 8(1+r)^4 = 200, where r represents the effective yield.
2. Solve for (1+r)^4 by dividing both sides of the equation by 8: (1+r)^4 = 25.
3. Take the common logarithm (log base 10) of each side of the equation: log((1+r)^4) = log(25).
4. Apply the power property of logarithms by multiplying the exponent inside the logarithm: 4 * log(1+r) = log(25).
5. Solve the equation for log(1+r) by dividing both sides by 4: log(1+r) = log(25)/4.
6. Use the exponential logarithmic inverse property, which states that if log(a) = b, then a = 10^b. Applying this property, we have 1+r = 10^(log(25)/4).
7. Solve for r by subtracting 1 from both sides of the equation: r = 10^(log(25)/4) - 1.
Now, to calculate the worth of a $1000 investment in stuffed fish in 3 years, follow these steps:
1. Use the formula: Future Value = Present Value * (1 + r)^t, where Present Value is $1000, r is the effective yield, and t is the number of years.
2. Substitute the values into the formula and solve: Future Value = $1000 * (1 + r)^3.
3. Use the value of r obtained from the previous calculation to find the Future Value.
Finally, to determine how long it will take until you can buy a $1800 computer, you'll need to know the expected effective yield on the investment. Once you have that value, follow these steps:
1. Use the formula: Future Value = Present Value * (1 + r)^t, where Present Value is the current worth of the investment, Future Value is the desired amount you want to reach, r is the effective yield, and t is the number of years.
2. Substitute the values into the formula and solve for t: t = log(Future Value/Present Value) / log(1+r).
3. Use the value of Future Value ($1800), Present Value (your current investment worth), and the expected effective yield to find the time it will take until you can purchase the $1800 computer.