Mr fish want to build a house in 10 years. he estimates that the total cost will be $170,000. if he can put aside 10,000 at the end of the year, what rate of return must he return must he earn in order to have the amount needed?
To calculate the rate of return Mr. Fish must earn in order to have the required amount, we need to use the concept of compound interest.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future amount (in this case, $170,000)
P = the principal amount (the initial investment)
r = annual interest rate (unknown in this case)
n = number of times interest is compounded per year (let's assume it's annually)
t = number of years
In this case, Mr. Fish plans to save $10,000 at the end of each year and wants to accumulate a total of $170,000 in 10 years.
Let's plug in the values we know:
A = $170,000
P = $10,000
t = 10
n = 1
Now we can rearrange the formula to solve for r:
r = (A/P)^(1/(n*t)) - 1
Substituting the values:
r = (170,000 / 10,000)^(1/(1*10)) - 1
Calculating the equation:
r = (17)^(1/10) - 1
Using a calculator, we can find:
r ≈ 0.413214 - 1
r ≈ -0.586786
Therefore, Mr. Fish would need to earn a negative return rate of -0.586786, which is not possible. It seems there may be an error or a missing piece of information in the given scenario.