raghav buys a shop for Rs. 1,20,000 he pays half of the amount in cash and agrees to pay the balance in 12 annual instalment of rs. 5000 each.if the rate of interest is 12% and he pays with the instalment the interest due on the unpaid amount,find the total cost of the shop.
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Given that Raghav buys a shop for 120000.
He pays half of the amount in cash = 1/2 * 120000
= 60000.
Balance amount to be paid = 120000 - 60000 = 60000.
Given that amount of each installment = 5000.
He agrees to pay the balance in 12 annual installments with interest of 12%.
1. Amount of the first installment = 5000 + 12/100 * 60000
= 5000 + 600 * 12
= 5000 + 7200
= 12200.
2. Amount of the second installment = 5000 + 12/100 * (60000 - 5000)
= 5000 + 12/100 * 55000
= 5000 + 550 * 12
= 5000 + 6600
= 11600.
So. the amount paid for installment is 12200,11600.......It forms an AP.
The 1st term a = 12200
Common Difference d = 11600 - 12200
= -600.
The number of terms n = 12.
We know that sum of n terms = n/2(2a + (n-1)* d)
Therefore the total cost of the shop = 60000 + 12/2(2(12200) + (12-1) * (-600))
= 60000 + 6(24400 - 6600)
= 60000 + 6 * 17800
= 60000 + 106800
= 166800.
The total cost of the shop = 166800.
Hope this helps!
He pays half of the amount in cash = 1/2 * 120000
= 60000.
Balance amount to be paid = 120000 - 60000 = 60000.
Given that amount of each installment = 5000.
He agrees to pay the balance in 12 annual installments with interest of 12%.
1. Amount of the first installment = 5000 + 12/100 * 60000
= 5000 + 600 * 12
= 5000 + 7200
= 12200.
2. Amount of the second installment = 5000 + 12/100 * (60000 - 5000)
= 5000 + 12/100 * 55000
= 5000 + 550 * 12
= 5000 + 6600
= 11600.
So. the amount paid for installment is 12200,11600.......It forms an AP.
The 1st term a = 12200
Common Difference d = 11600 - 12200
= -600.
The number of terms n = 12.
We know that sum of n terms = n/2(2a + (n-1)* d)
Therefore the total cost of the shop = 60000 + 12/2(2(12200) + (12-1) * (-600))
= 60000 + 6(24400 - 6600)
= 60000 + 6 * 17800
= 60000 + 106800
= 166800.
The total cost of the shop = 166800.
Hope this helps!
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