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?
Under these conditions how long will it be before you can buy your computer? Explain how you found your answer.
You don't even need logs to do that question. From...
8(1+r) ^4=200
(1+r)^4 = 25
take the fourth root, (take the square root twice in a row) to get
1 + r = 2.236058
r = 1.236
the rate of return is 123.6% (wow)
so $1000 invested at that rate for 3 years would have a value of
1000(2.236)^3
= $11,180.34
To find the effective yield for the investment, follow these steps:
1. Begin with the equation: 8(1+r)^4 = 200. This equation represents the initial investment ($8) compounded at a rate of (1+r) for 4 years, resulting in a final value of $200.
2. Solve for (1+r)^4: Divide both sides of the equation by 8: (1+r)^4 = 200/8 = 25.
3. Take the common logarithm of each side of the equation: log((1+r)^4) = log(25).
4. Use the power property of logarithms to rewrite log((1+r)^4): 4 * log(1+r) = log(25).
5. Solve the equation for log(1+r): Divide both sides of the equation by 4: log(1+r) = log(25)/4.
6. Use the exponential logarithmic inverse property to eliminate the logarithm: Raise both sides of the equation as the base 10 exponent: 10^(log(1+r)) = 10^(log(25)/4).
7. Simplify: 1+r = 10^(log(25)/4).
8. Solve for r: Subtract 1 from both sides of the equation: r = 10^(log(25)/4) - 1.
Now that we have found the value of r, we can calculate the future value of a $1000 investment in stuffed fish in 3 years:
1. Determine the effective yield, r, using the steps mentioned above.
2. Use the formula: Future Value = Present Value * (1+r)^n, where n is the number of years.
3. Plug in the given values: Present Value = $1000, n = 3, and the calculated value of r.
4. Calculate: Future Value = $1000 * (1 + r)^3.
To find out how long it will take before you can buy your computer, we need more information about the computer's price and the amount you can invest per year. With that information, we can calculate how many years it will take for your investments to accumulate enough to purchase the computer.