You currently have $7,500 to invest. You can invest the full amount now for a periodof 9 years at which time you want to have $15,000. Approximately what rate ofreturn is needed to accomplish this investment goal?
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To determine the approximate rate of return needed to accomplish this investment goal, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Future value of the investment ($15,000)
P = Principal amount invested ($7,500)
r = Annual interest rate (to be determined)
n = Number of times the interest is compounded per year (typically 1 for annual compounding)
t = Number of years (9)
Rearranging the formula to solve for r, we have:
r = (A/P)^(1/(n*t)) - 1
Substituting the given values, we have:
r = (15000/7500)^(1/(1*9)) - 1
Simplifying the equation:
r = 2^(1/9) - 1
Using a calculator to evaluate this expression, the approximate rate of return needed to reach $15,000 in 9 years with a $7,500 investment is about 8.08%.
Therefore, an approximate rate of return of 8.08% per year is needed in order to accomplish this investment goal.
Pt = Po + Po*rt,
Pt = Po(1+rt),
7500(1+9r) = 15,000.
Divide both sides by 7500:
1 + 9r = 2,
9r = 2 - 1 = 1.
r = 1 / 9 = 0.111 = 11.111%.