Question

A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?

Answer 1

16680

Step-by-step explanation:

Amount Paid to buy tractor = Rs. 12,000

Farmer Pays Cash = Rs. 6000

Remaining Balance = 12000 - 6000 = 6000

Annual Instalment = Rs 500 + interest@12% on unpaid amount

1st Instalment

Unpaid Amount = Rs. 6000

Interest on Unpaid Amount = (12/100) × 6000 = 720

Amount of Instalment = Rs. 500 + Rs. 720 = Rs. 1220

2nd Instalment

Unpaid Amount = Rs. (6000 - 500) = Rs. 5500

Interest on Unpaid Amount = (12/100) × 5500 = 6600

Amount of Instalment = Rs. 500 + Rs. 660 = Rs. 1160

3rd Instalment

Unpaid Amount = Rs. (5500 - 500) = Rs. 5000

Interest on Unpaid Amount = (12/100) × 5000 = 600

Amount of Instalment = Rs. 500 + Rs. 600 = Rs. 1100

Total no. of Instalments = 6000/500 = 12

Thus, Annual Instalments are 1220, 1160, 1100, …upto 12 terms

Since the common difference between the consecutive terms is constant. Thus, Annual Instalments are in AP.

Here

first term(a) = 1220

Common difference(d) = 1160 - 1220 = - 60

Number of terms(n) = 12

Total amount paid in 12 instalments is given by -

Sn = (n/2)[2a + (n - 1)d]

∴ S12 = (12/2)[2(1220) + (12 - 1)( - 60)]

= 6[2440 + 11( - 60)]

= 6[2440 - 660]

= 6 × 1780

= 10680

Hence, total amount paid in 12 Instalments = Rs 10680

Hence,

Total Cost of Tractor

= Amount paid earlier + Amount paid in 12 Instalments

= Rs. (6000 + 10680)

= Rs. 16680

JAI SHREE KRISHNA

Answer 2

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A farmer buys a used tracto...

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A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installment of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him

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ANSWER

Given farmer buys a tractor for Rs. 12,000 and pays Rs 6,000 in cash

⇒ Unpaid amount =12000−6000=Rs6,000.

At the end of the first year, interest paid =12% of 6000

Amount paid as installment at the end of 1 year =Rs500.

So, loan amount left =Rs6000−500=Rs5,500

Now, at the end of the second year, interest paid 12% of 5500

Amount paid as installment at the end of the second year = Rs500

So, loan amount left =Rs5500−500=Rs5000

So, total interest to be paid =12% of 6000+12% of 5500+12% of 5000+...+12% of 500.

=12% of (6000+5500+5000+...+500)

=12% of (500+1000+1500+...+5500+6000) ....(1)

Here, 500,1000,1500,...6000 form an A.P. with both the first term and common difference equals to 500.

Let the number of terms of A.P.be n.

∴6000=500+(n−1)(500)

⇒n=12

∴S

12

=500+1000+1500+...+6000

we know, Sum (S

n

)=

2

n

[2a+(n−1)d]

∴S

12

=

2

12

[2(500)+(12−1)(500)]

=6[1000+5500]=39000

So, by eqn(1),

Total interest paid =12% of (500+1000+1500+...+6000)

=12% of Rs.39,000

=Rs.4,680

So, the cost of the tractor to him is Rs.12000+4680=Rs16,680

Step-by-step explanation:

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