Question

Suppose you have $14,000 to invest Which of the two rates would yield the larger amount in 2 years 6% compounded monthly or 5.88% compounded continuously?

Answer 1

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:

`A=P(1+(r)/(12))^(12\cdot t)`

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:

`A=P\cdot e^(t\cdot r)`

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:

`\begin{gathered} A_1=14000\cdot(1+(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}`
`\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}`

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.