Respuesta :
We were given a principal to invest ($14,000) in a timespan of 2 years, and we need to choose between applying it on an account that is compounded montlhy at a rate of 6%, and one that is compounded continuously at a rate of 5.88%. To solve this problem, we need to calculate the final amount on both situations, and compare them.
The expression used to calculate the amount compounded monthly is shown below:
[tex]A=P(1+\frac{r}{12})^{12\cdot t}[/tex]Where A is the final amount, P is the invested principal, r is the interest rate and t is the elapsed time.
The expression used to calculate the amount compounded continuously is shown below:
[tex]A=P\cdot e^{t\cdot r}[/tex]Where A is the final amount, P is the invested principal, r is the interest rate, t is the elapsed time, and "e" is the euler's number.
With the two expressions we can calculated the final amount on both situations, this is done below:
[tex]\begin{gathered} A_1=14000\cdot(1+\frac{0.06}{12})^{12\cdot2} \\ A_1=14000\cdot(1+0.005)^{24} \\ A_1=14000\cdot(1.005)^{24} \\ A_1=14000\cdot1.127159 \\ A_1=15780.237 \end{gathered}[/tex][tex]\begin{gathered} A_2=14000\cdot e^{0.0588\cdot2} \\ A_2=14000\cdot e^{0.1176} \\ A_2=14000\cdot1.124794 \\ A_2=15747.12 \end{gathered}[/tex]The first account, that is compounded monthly yields a return of $15780.24, while the second one that is compounded continuously yields a return of $15747.12, therefore the first account is the one that yield the larger amount in 2 years.
