Question

Simply Savings Bank offers a simple interest rate of 10% per year. Compound Capital Bank offers an interest rate of 8% per year compounded continuously. If Shakira plans to invest $200 for 5 years, which bank should she choose?

Answer 1

She should choose the Simply Savings Bank, since she'll earn around 2 dollars more in comparison to the other bank.

Explanation:

A simple interest rate account yields a return that follows the formula below:

`return = C + C*r*t`

Where C is the invested money, r is the interest rate and t is the elapsed time in years.

While a compound interest rate account yields a return that follows the formula below:

`return = C*e^(r*t)`

Therefore for the Simply Saving Bank she'll earn:

`return_(1) = 200 + 200*0.1*5\\return_(1) = 200 + 100\\retrun_(1) = 300`

While the Capital Bank she'll earn:

`return_2 = 200*e^(0.08*5)\\return_2 = 200*e^(0.4)\\return_2 = 200*1.49182\\return_2 = 298.364`

She should choose the Simply Savings Bank, since she'll earn around 2 dollars more in comparison to the other bank.