Respuesta :
Answer:
The time it will take for the account balance to reach $3,726.18 is 15 months.
Step-by-step explanation:
The information provided is:
- Jaidee invests $2,628 in a retirement account
- With a fixed annual interest rate of 2.33%
- Compounded 12 times per year, i.e. compounded monthly.
- Final account balance: $3,726.18
The formula of compound interest (compounded monthly) is:
[tex]A=P(1+\frac{r}{12})^{12t}[/tex]
Compute the value of t as follows:
[tex]3726.18=2628\times (1+\frac{0.0233}{12})^{12t}\\\\\frac{3726.18}{2628}= (1.00194167)^{12t}\\\\1.41787671= (1.00194167)^{12t}\\\\\log(1.41787671)= 12t\times \log(1.00194167)\\\\12t=\frac{\log(1.41787671)}{\log(1.00194167)}\\\\t=14.99995\\\\t\approx 15[/tex]
Thus, the time it will take for the account balance to reach $3,726.18 is 15 months.
