Question

F1 A farmer borrowed Rs. 60,000 and agreed to repay with interest in a year in twelve monthly installments.The first instalment was Rs.12,000. The next each installment was less than the prceding one by Rs.1000.Find the total amount he paid in the whole year. What was the inerest charged? Find the rate of interest charged per annum.(simple interest)

Answer 1

• First, we find the amount he paid in 12 monthly installments.

       We know,

        aₙ = a+(n-1)d

        here, a=12000, d = -1000 and n=12.

d is negative as the next installment is less than the              preceding one by 1000.

So, this gives, aₙ = 12000 - 11000 = 1000.

• Now, the amount paid by him in total is given by,

        Sₙ = n/2 (a+aₙ)

        Putting values,

        S= 6(13000) = 78000

So, the amount paid by him was 78000.

• Now, Simple Interest = 78000-60000 = 18000

        And we know, SI=PRT/100

So, R or rate = 1800000/60000 = 30%

Answer 2

Answer:

The Amount paid in whole year is Rs 78,000

The rate of interest is 30%  

Step-by-step explanation:

Given as :

The borrowed principal = Rs 60,000

The time period = 1 years = 12 months

First installment amount = Rs 12,000

The next installment amount was less than preceding by Rs 1000

So, The second installment must be = rs 12,000 - rs 1000 = Rs 11,000

So, The installment payment are Rs 12,000 , Rs 11,000 , Rs 10,000 ...so on

Now,

Sum of nth term of payment = $s_n$

i.e $s_n$ = a + (n - 1) d

where a is first term

d is common difference

Or, a = rs 12,000  , d = - rs 1000

So, $s_12$ = $\dfrac{n}{2}$ × [ 2 a + ( n - 1 ) d ]

or, $s_12$ = $\dfrac{12}{2}$ × [ 2 × 12,000 + ( 12 - 1 ) ( - 1000 )]

Or, $s_12$ = 6 × [ 24,000 - 11000 ]

Or, $s_12$ = 6 × 13,000

∴   Or, $s_12$ = Rs 78,000

So, The Amount paid in 12 months installment = $s_12$ = Rs 78,000

∵ Principal borrowed = Rs 60,000

We know that

Interest = Amount - Principal

i.e Interest = Rs 78,000 - Rs 60,000

∴ Interest credit = Rs 18,000

So, The interest credited to borrowed amount = Rs 18,000

And Total amount paid in whole year = Principal + Interest

i.e Amount = Rs 60,000 + Rs 18,000

Or, Amount = Rs 78,000

Again

Let The rate of interest = R % simple interest

So, Simple Interest = $\dfrac{principal\times rate\times time}{100}$

i.e Rs 18,000 = $\dfrac{Rs 60,000\times R\times 1}{100}$

Or, Rs 60,000 × R = Rs 18,00000

∴  R = $\dfrac{1800000}{60000}$

i.e R = 30%

Hence, The Amount paid in whole year is Rs 78,000 and The rate of interest is 30%   Answer