Answer:
To determine the number of years it will take for a $5000 investment to reach $7500 at an 8% interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value (in this case, $7500)
P is the principal amount (in this case, $5000)
r is the interest rate (in decimal form, so 8% would be 0.08)
n is the number of times interest is compounded per year (assuming annually, so n = 1)
t is the number of years
We need to solve for t in this equation. Rearranging the formula to isolate t, we get:
t = (log(A/P)) / (n * log(1 + r/n))
Plugging in the values:
t = (log(7500/5000)) / (1 * log(1 + 0.08/1))
Calculating this equation will give us the number of years it will take for the investment to reach $7500.
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