You have an investment opportunity which yields 9% per year. About how many years will it take your initial investment of $10,000 to grow to a total of of $40,000? Please give your answer as a whole number

Pt = 10000 + 10000*0.09*t = 40000.

900t = 40000-10000 = 30000.
t = 30000 / 900 = 33.33 Years or 33yrs.

Use financial calculator to solve for the interest rate involved in the following future value of an annuity due problem. The future value is $57,000, the annual payment is $7,500, and the time period is six years

To calculate the number of years it will take for an investment to grow to a desired amount, you can use the compound interest formula:

A = P(1 + r/n)^(n*t)

Where:
A is the final amount (in this case $40,000)
P is the initial investment (in this case $10,000)
r is the annual interest rate (in this case 9% or 0.09 as a decimal)
n is the number of times interest is compounded per year (assuming it's compounded once per year, so n = 1)
t is the number of years

Rearranging the formula to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Let's plug in the values:

t = (log(40000/10000)) / (1 * log(1 + 0.09/1))

Calculating this equation will give us the answer.