forms of expressions and equations

Question

Carrie deposits $2,500 in a bank. It pays 0.07% interest per week on deposits. The function f represents the amount in Carrie’s account after t years. Which of the following functions is given in a form that clearly reveals the approximate annual interest rate?

Answer 1

First let's find the annual interest rate. Remember that in this case, each week you will be multiplying "1.0007" (100%+0.07%) to the balance of the previous week. Since each year has 365 days or approximately 52 weeks, the annual interest rate turns out to be: (1.0007)⁵²=1.03705, so the annual rate its 3.705%.

The same concept applies to the balance at the end of each year, the balance of the precious year will be multiplied by a factor of "1.0375" or 100%+3.705% which is done once every year.

The balance in the account is as follows:

Balance=($2,500)(1.03705)^y