Final answer:
Using the compound interest formula, we calculate that it will take approximately 7.93 years for Jen's $800 investment to grow to $3,600 at an interest rate of 8.75% when compounded annually.
Step-by-step explanation:
To calculate the number of years it will take for Jen to grow her $800 investment to $3,600 at an interest rate of 8.75%, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
In Jen's case, the account is likely compounded once a year (n=1) which simplifies our formula to:
A = P(1 + r)^t
We are given:
A = $3,600
P = $800
r = 8.75% or 0.0875
We need to solve for t:
$3,600 = $800(1 + 0.0875)^t
To find t, we can use logarithms:
log($3,600/$800) = t * log(1 + 0.0875)
t = log($3,600/$800) / log(1 + 0.0875)
Calculating this gives us the number of years t needed for Jen's investment to reach $3,600.
By inputting the values into a calculator, we get:
t = log(4.5) / log(1.0875) ≈ 7.93 years
Therefore, it will take approximately 7.93 years for Jen's account to reach $3,600 given an 8.75% annual interest rate.