Question

Hari borrowed \[{\rm{Rs}}12,600\] from a moneylender at \[15\% \] per annum simple interest. After 3 years, he paid \[{\rm{Rs}}7,070\] and gave a goat to clear off the debt. What is the cost of the goat?

Answer 1

Hint: Here, we will first substitute the given values in the formula of simple interest to find the interest incurred on the borrowed money. We will then add the obtained interest to the borrowed money to find the amount to be paid back. Then we will subtract the amount he paid from the obtained amount to find the required cost of the goat.

Formula Used:
We will use the formula \[S.I = \dfrac{{P \cdot R \cdot T}}{{100}}\], where \[S.I\] is the Simple Interest, \[P\] is the Principal, \[R\] is the rate of interest per annum and \[T\] is the time period.

Complete step-by-step answer:
According to the question,
Sum of money borrowed by Hari from the moneylender, i.e. Principal, \[P = {\rm{Rs}}12,600\]
Hari had borrowed this principal at \[15\% \] per annum. Therefore,
The rate of interest per annum, \[R = 15\% \]
Also, he paid back the amount after 3 years.
Thus, the time period for which the principal has been borrowed, \[T = 3\] years
Now, it is given that Hari had borrowed the principal at simple interest.
Substituting \[T = 3\], \[P = {\rm{Rs}}12,600\] and \[R = 15\] in this formula \[S.I = \dfrac{{P \cdot R \cdot T}}{{100}}\], we get,
\[S.I = \dfrac{{12600 \times 15 \times 3}}{{100}}\]
Dividing the numerator by 100, we get
\[ \Rightarrow S.I = 45 \times 126 = 5670\]
Therefore, Simple Interest after 3 years is \[{\rm{Rs}}5670\].
Now we will calculate the amount to be paid back which is equal to the sum of principal and the interest incurred on it.
The total amount to be paid back \[ = P + S.I\]
As, Hari will be required to pay back the sum of money borrowed along with the interest on that money.
Substituting Principal, \[P = {\rm{Rs}}12,600\]and Simple Interest, \[S.I = {\rm{Rs}}5670\] in the bove equation, we get
The total amount to be paid back \[ = 12600 + 5670 = {\rm{Rs}}18270\]
But according to the question, Hari paid \[{\rm{Rs}}7,070\] after 3 years.
Thus, amount left to be paid \[ = 18270 - 7070 = 11200\]
But, he also gave a goat to clear off the debt.
Thus the cost of goats would be the amount left to be paid.
Therefore, the cost of the goat \[ = {\rm{Rs}}11200\].
Hence, this is the required answer.

Note: In this question we have used the formula of Simple Interest. Simple Interest is the interest earned on the Principal or the amount of loan. The second type of interest is Compound Interest. Compound Interest is calculated both on the Principal as well as on the accumulated interest of the previous year. Hence, this is also known as ‘interest on interest’.