Question

Find the amount to be paid at the end of 2 years on Rs. 2400 at 5% per annum compounded annually.

Answer 1

Hint: We need the formula for finding the amount. We use the formula \[A = P{ \left[ {1 + \dfrac{r}{{100}}} \right] ^n} \] where, \[A \] is the amount, \[P \] is principal amount, \[r \] is the rate percent yearly (or every fixed period) and \[n \] is the number of years (or terms of the fixed period). Since all the values are given, substituting in the above formula we get the required amount.

Complete step-by-step answer:
List out the given data, that is
Rate per annum, \[r = 5 \]
Principle amount, \[P = 2400 \]
Number of years, \[n = 2 \]
The amount to be paid in case of compound interest is \[A = ? \]
We know the formula,
  \[A = P{ \left[ {1 + \dfrac{r}{{100}}} \right] ^n} \]
Substituting we get,
 \[ \Rightarrow A = 2400{ \left[ {1 + \dfrac{5}{{100}}} \right] ^2} \]
Taking L.C.M. in bracket and simplify, we get:
 \[ \Rightarrow A = 2400{ \left[ { \dfrac{{105}}{{100}}} \right] ^2} \]
Since square is there in the bracket, simplify it, we get:
 \[ \Rightarrow A = 2400{ \left[ { \dfrac{{21}}{{20}}} \right] ^2} \]
Removing square, we get:
 \[ \Rightarrow A = 2400 \left[ { \dfrac{{21 \times 21}}{{20 \times 20}}} \right] \]
Simply separating the numerator and denominator terms,
 \[ \Rightarrow A = \dfrac{{2400 \times 21 \times 21}}{{400}} \]
Simple division, we get:
 \[ \Rightarrow A = 6 \times 21 \times 21 \]
Multiplying we get,
 \[ \Rightarrow A = 2646 \] .
Hence the required amount is 2646 rupees.
That is, the amount Rs. 2646 to be paid at the end of 2 years on Rs. 2400 at 5% per annum compounded annually.
So, the correct answer is “2646”.

Note: If they ask for an amount to be paid in three year, just put n=3 and follow the same procedure. Students need to remember the formula so that you can solve the problem for different years, different rates of interest and as well as for different principal amounts. Carefully substitute the values. Principal amount is the money that you originally agreed to pay back.