Question

If you invest \[2000\] offering \[10\% \] interest compounded weekly. How do you find the value of your investment after \[5\] years?

Answer 1

Hint: The compound interest given here is $ 10\% $ per annum but it is compounded weekly so we see that there is compounding of the investment $ 52 $ times in a given year but since we have to tell the value of investment after $ 5 $ years the total times the investment will be compounded will be calculated to be as
 $ 52*5 $ which is a total of $ 260 $ times . Also the interest will be calculated weekly from $ 10\% $ per annum so we will also have to calculate the interest percent per week which can be calculated by dividing the given interest percent by the number of weeks in a year (which means $ 52 $ times). Then we will calculate the amount by using the standard formula which is \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\] where $ A $ is the amount which we have to calculate according to the question.

Complete step by step solution:
Since the interest is compounded weekly we can say approximately the interest will be compounded $ 52 $ times in a year and $ 260 $ times in a year also the effective interest for a week will be calculated as:
Interest= \[\dfrac{{10}}{{52}}\% \] thus we will now calculate the amount which we will receive after $ 5 $ years using the standard formula which is as follows:
 \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\] where $ A $ is the amount which we are calculating, $ P $ is the principal which is given as $ 2000 $ and r is the rate of interest which we have calculated as \[\dfrac{{10}}{{52}}\% \] and $ n $ is the number of time intervals which we have calculated as $ 260 $ so we calculate amount as follows:
 \[A = 2000{\left( {1 + \dfrac{{\dfrac{{10}}{{52}}}}{{100}}} \right)^{260}}\] which can then be written as
 \[A = 2000{\left( {1 + \dfrac{{10}}{{5200}}} \right)^{260}}\] upon solving we get
 \[A = 3295.86\]
Which is the final answer.
So, the correct answer is “ \[A = 3295.86\]”.

Note: When calculating compound interest always remember to find the effective rate of interest in the case that interest is not compounded annually without calculating it we will get wrong results.