Question

At what rate percent will $Rs.1600$ amounts to $Rs.2000$ in $5$ years.

Answer 1

Hint: First, we need to know about the concept of simple interest. Which is the technique of computing the amount of the interest for a principal amount of money at some rate of interest. Where P refers to the principal amount, T refers to the time taken on the process, R is the rate of the interest percent per annum.

Formula used: The Simple interest formula is $S.I = \dfrac{{P \times R \times T}}{{100}}$ and note that calculating the amount formula is $A = P + SI$

Complete step-by-step solution:
Since from that we need to find the percentage of the $Rs.1600$ amounts to $Rs.2000$ in $5$ years. This means we need to find the rate of change per annum and refer to R.
Also given that the time is $T = 5$ and principal amount $P = 1600$ and A is the amount that changes (increased)
Hence to find the simple interest we use the second formula given above $A = P + SI$ where $A = 2000$ and $P = 1600$, I is the interest.
Hence, we have $SI = A - P = 2000 - 1600 = 400$ is a simple interest.
Hence substituting all the values into the formula, we have $S.I = \dfrac{{P \times R \times T}}{{100}} $
$\Rightarrow 400 = \dfrac{{1600 \times R \times 5}}{{100}}$
Further solving we get,
 $400 = 16 \times R \times 5$
$ \Rightarrow R = \dfrac{{400}}{{16 \times 5}} $
$\Rightarrow R= 5\% $
Hence the rate of change interest is $5\% $
Therefore $5\% $ rate percent will $Rs.1600$ amount to $Rs.2000$ in $5$ years.

Note: We also need to know about the concepts of the percentage. The percentage is the mathematical concept which is to measure the proportion of the given values in any term of the original value. The percentage is a relative value that indicates the hundredth parts of any quantity.
The compound interest formula is $A = P{(1 + \dfrac{r}{n})^{nt}}$ where T is the time taken, P is the principal amount, R is the rate of change per annum.