Question

Suppose that you deposit $ 9000 in a savings account that pays 3 % annual​ interest, with interest credited to the account at the end of each year. Assuming that no withdrawals are made and that interest is compounded​ annually, complete parts ​(a) and ​(b) below.
​(a) Find the balance in the account after 5 years.
​(b) Find the balance in the account after 9 years and 7 months.

Answer 1

We use the formula $A=P\left(1+\dfrac{r}{n}\right)^{nt}$, where

   A is the ending amount or value
   P is the initial amount of investment or deposit 
   r is the annual/nominal interest rate
   n is the number of compoundings per year
   t is the number of years.

For Part A:

This formula becomes $A=9000\left(1+\dfrac{0.03}{1}\right)^{1\cdot 5}$.  In this case A ≈ 10,433.67.

For Part B:

Based on the statement that "interest (is) credited to the account at the end of each year," I have to assume that the 7 months after the 9th complete year do not earn any interest.  With that understanding, we have

      $A=9000\left(1+\dfrac{0.03}{1}\right)^{1\cdot 9}\approx11,742.96$

Now if it was intended for the interest to be earned on that portion of a year, then your t-value would be $9\frac{7}{12}$ or $\frac{115}{12}$ and your calculation would be
    $A=9000\left(1+\dfrac{0.03}{1}\right)^{1\cdot \frac{115}{12}}\approx11,947.19$

Again, I do not think that second option is correct based on interest being credited at the end of the year.