15.Pedro Martinez wants to invest $25,000 in a spa that his sister is starting. He will triple his investment in six years. What is the rate of return that Pedro is being promised
solve for i
1(1+i)^6 = 3
i got i = .4422
so 44.22% ??? wow!
To find the rate of return that Pedro is being promised, we need to calculate the annual growth rate of his investment over six years.
To triple an investment means to achieve a 200% return, as initially Pedro invests $25,000 and wants to triple that amount.
We can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, Pedro wants to triple his investment, so the future value (A) is 3 times his initial investment, which is $75,000 ($25,000 * 3).
Plugging in the values into the formula, we have:
$75,000 = $25,000(1 + r/1)^(1 * 6)
Simplifying this equation, we get:
3 = (1 + r)^6
Next, we need to isolate the term with the interest rate (r). Taking the sixth root on both sides of the equation gives us:
(1 + r) = ∛3
Finally, subtracting 1 from both sides yields:
r = ∛3 - 1
So, the rate of return that Pedro is being promised is approximately ∛3 - 1, which can be calculated using a calculator or estimated to be around 0.44224957 (or approximately 44.22%).