Final answer:
To find out how long it will take for Janet's $3200 deposit to triple in value at a 4.5% interest rate, we use the compound interest formula. By solving for time t, which is approximately 24.93 years, we know it will take nearly 25 years for the investment to triple.
Step-by-step explanation:
Calculating the Time to Triple an Investment
Janet deposited $3200 at an annual interest rate of 4.5%. To determine how long it will take for her investment to triple, we use the formula for compound interest:
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 in years.
In Janet's case, we want to find the value of t when the investment has tripled. So, A = 3 × P:
3 × $3200 = $3200(1 + 0.045)^t
Divide both sides by $3200:
3 = (1 + 0.045)^t
Now, we take the logarithm of both sides to solve for t:
log(3) = t × log(1.045)
t = log(3) / log(1.045)
Using a calculator, we find that t is approximately 24.93 years.
Therefore, at a 4.5% annual interest rate, it will take close to 25 years for Janet's investment to triple.