Question

A bank charges Rs. 6 for a loan of Rs. 120. The borrower receives Rs. 114 and repays the loan in 12 installments of Rs. 10 a month. The interest rate is approximate?
(a) 5 %
(b) 15 %
(c) 1 %
(d) 4 %

Answer 1

Hint: The given question can be directly solved by using the formula, \[A=P{{\left( 1+\dfrac{r}{100n} \right)}^{nt}}.\] Here in the given formula, A is the amount or total loan to be paid by the borrower, P is the loan originally taken by the borrower, r is the rate, n is the number of installments and t is the time in years.

Complete step by step answer:
In the question,it is given that a bank charges Rs. 6 for a loan of Rs. 120. The borrower receives Rs. 114 and repays the loan in 12 installments of Rs. 10 a month and we have to find the interest rate of approximation. The person who is asking the loan gets a sum of Rs. 114 from the giver of the loan.
In the next portion, we see that the borrower pays Rs. 10 a month in 12 installments which means he gave the book.
The total price of Book = Rs. 120
So, the sum of money paid is Rs. 120.
We will find the rate of interest using the formula,
The total sum of money paid \[=P{{\left( 1+\dfrac{r}{100n} \right)}^{nt}}\]
Here, P is the amount the borrower got, r is the rate which we need to find out, n is the number of installments, t is the time in years.
Here, P is Rs. 114, n = 12, t = 1 year
So, substituting these values, we get,
\[120=114{{\left( 1+\dfrac{r}{1200} \right)}^{12}}\]
So on dividing 114, from both the sides, we get,
\[\dfrac{120}{114}={{\left( 1+\dfrac{r}{1200} \right)}^{12}}\]
We can further write it as,
\[{{\left( \dfrac{120}{114} \right)}^{\dfrac{1}{12}}}=1+\dfrac{r}{1200}\]
On calculation, we get,
\[1.0042836=1+\dfrac{r}{1200}\]
Now, subtracting 1 from both the sides, we get,
\[\dfrac{r}{1200}=0.0042836\]
On cross multiplying, we get,
\[r=5.14\]
So approximately, the rate of interest is 5 %.
Hence, the correct option is (a).

Note:
One can also imagine or do the given sum like this. Students can also take the loan or amount to be paid as the amount (A), the principle (P) as the money/amount taken by the borrower, the number of installments will be taken as n and rate r will be the applied rate by the lender divided by n and the time t will be the product of time taken to pay the loan and n and hence use the formula
\[A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}\]