Hello Steve, it didn't work for "t" i can't get the actual value...
Find the time required for an investment of 1 dollars to grow to 7200 dollars at an interest rate of 7.5 percent per year, compounded quarterly
7200=1(1+ .075/4)^t/4 where t is in years.
You actually want one dollar to grow to 7500?
take log of each side
log 7200=t/4 (log 1.018)
t=4* log7200/log1.018=1991 years
Hello Bobpursley, it still didn't work. it says wrong answer. Thanks
^4t not to the t/4
1.01875^4t = 7200
4 t = log 7200/log 1.01875
t = 120 years
Hello Damon, thanks a lot. But it says incorrect.
To find the time required for the investment to grow to $7200, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($7200)
P = the principal investment ($1)
r = the annual interest rate (7.5% or 0.075 as a decimal)
n = the number of times the interest is compounded per year (quarterly, so 4)
t = the number of years
We need to solve for t in this equation. Rearranging the formula to solve for t:
t = (ln(A/P) / (n * ln(1 + r/n)))
Now, let's plug in the values:
t = (ln(7200/1) / (4 * ln(1 + 0.075/4)))
Calculating the value inside the natural logarithm:
t = (ln(7200) / (4 * ln(1 + 0.075/4)))
Using a calculator to evaluate the expression:
t ≈ 18.78
Therefore, it will take approximately 18.78 years for the investment of $1 to grow to $7200 at an interest rate of 7.5% per year, compounded quarterly.