Question

Jacob invests Rs $12000$ for $3$ years at $10$% per annum. Calculate the amount and the compound interest that Jacob will get after $3$ years.

Answer 1

Hint: First, we have found the interest for the first year, and then calculate the amount at the end of first year. Similarly find the interest and amount for the second and third year using simple interest formula and amount formula. Finally we find the compound interest after \[3\] years and we will get the required answer.

Formula used: Amount = Principal + Interest.
Simple Interest$ = \dfrac{{{\text{Principal }} \times {\text{ Rate }} \times {\text{ Time}}}}{{100}}$
Compound interest = Final amount – Original Principal.

Complete step-by-step solution:
It is given that the question stated the value of principal, rate and time.
Since we called the money invested is called principal.
So, we can write it as the principal = Rs $12000$.
Also, rate is the interest paid on Rs $100$ for a specific period.
It is given that the rate = $10$% per annum.
Also, it is given that the time for investing Rs $12000$ is $3$ years.
In mathematically we can write it as, Time = $3$ years.
Now we have to find the interest for the first year using the formula for Simple interest
That is we can write it as, $ = \dfrac{{{\text{Principal }} \times {\text{ Rate }} \times {\text{ Time}}}}{{100}}$
Putting the given values and we get,
Interest for the first year = Rs $\dfrac{{12000 \times 10 \times 1}}{{100}}$
On simplification we get
\[ \Rightarrow \]Rs $1200$
Also, we have to find the amount at the end of first year using the amount formula,
So we can write it as Amount = Principal + Interest.
Amount at the end of first year = Rs $12000$ + Rs $1200$
Let us add the terms and we get
\[ \Rightarrow \]Rs $13200$
Again we can find the interest for the second year using Simple interest
$ \Rightarrow \dfrac{{{\text{Principal }} \times {\text{ Rate }} \times {\text{ Time}}}}{{100}}$.
Use the new Principal amount at the end of first year = Rs $13200$
Time \[ = 1\] year
Putting the value and we get
Interest for the second year = Rs $\dfrac{{13200 \times 10 \times 1}}{{100}}$
On simplification we get
$ \Rightarrow $ Rs $1320$
Similarly we can find the amount at the end of second year using Amount = Principal + Interest.
Amount at the end of second year = Rs $13200$ + Rs $1320$
$ \Rightarrow $ Rs $14520$
Find the interest for the third year using Simple interest $ = \dfrac{{{\text{Principal }} \times {\text{ Rate }} \times {\text{ Time}}}}{{100}}$.
Use the Principal amount for end of the second year = Rs $14520$
Putting the values and we get
Interest for the third year = Rs $\dfrac{{14520 \times 10 \times 1}}{{100}}$
On simplification we get,
$ \Rightarrow $ Rs $1452$
Find the amount at the end of third year using Amount = Principal + Interest.
Amount at the end of third year = Rs $14520$ + Rs $1452$
Let us add the term and we get
$ \Rightarrow $Rs $15972$
Now we have to find out the compound interest for $3$ years.
Compound interest for $3$ years = Final amount – (original) Principal
$ \Rightarrow $Rs $15972$ - Rs $12000$
On subtracting we get
$ \Rightarrow $ Rs $3972$
Thus, the amount and the compound interest that Jacob will get after $3$ years are Rs $15972$ and Rs $3972$ respectively.

Note: Under Compound Interest, the interest is added to the principal at the end of each period to arrive at the new principal for the next period.
In other words, the amount at the end of first year (or period) will become the principal for the second year (or period); the amount at the end of second year (or period) becomes the principal for the third year (or period) and so on.