My opinion is that the teacher is
incorrect.
Using the knowledge of business finance (the future value of
money), it is important to note how many time(s) the interest is /
are being compounded /counted in a year.
(1) When the interest is compounded/ counted once a year
the formula is P = A [ 1 + (i/100) ] ^ n
(2) When the interest is compounded / counted every month
ie 12 times in a year, the formula is P = A [ 1 + ( { i / 12 } /100) ] ^ ( n x12
)
(3) When the interest is compounded / counted every 6 months ie 2
times in a year, the formula is P = A [ 1 + ( { i / 2 } /100) ] ^ ( n x 2
)
For the question, it is stated that the bank paid a compound
interest of 2.8% per annum ie the interest is to be counted once at
the end of every year.
So, there is no extra interest
earned (since this is not yet one whole of the first year) on
interest paid which is the concept of compound interest.
Hence, the simple interest is to
be used for this question ie
Total
amount at the end of 6 months
= 5000 + 5000 x (2.8/100) x (6/12)
= $5070
In addition, the amount calculated on a compound interest basis
MUST always be GREATER
than the amount calculated on a simple interest
basis.
It is to be noted that the teacher's
answer of $5069.52 is less than $5070.