A person buys a refrigerator for rupees 12000. He pays rupees 6000 in cash and agrees to pay the balance in 12 annual instalments of rupees 500 each. If the rate of interest is 12% and he pays it with instalments on the unpaid amount,
how much did the refrigerator cost him
To calculate the total cost of the refrigerator, we need to consider the principal amount, the interest, and the instalments paid.
The principal amount is the initial cost of the refrigerator, which is Rs. 12,000.
The person pays Rs. 6,000 in cash, so the remaining principal amount is Rs. 12,000 - Rs. 6,000 = Rs. 6,000.
The remaining principal amount is to be paid in 12 annual instalments of Rs. 500 each, considering that the interest is paid on the unpaid amount.
First, let's calculate the interest on the remaining principal amount. The interest rate is 12% per annum, and it is compounded annually.
To find the interest for one year, we can use the formula:
Interest = Principal × Rate of Interest
So, for the first year, the interest is:
Interest = Rs. 6,000 × 12% = Rs. (6,000 × 0.12) = Rs. 720
The instalment of Rs. 500 is paid annually. So, after the first year's payment, the remaining amount to be paid is:
Remaining Amount = Principal + Interest - Instalment
Remaining Amount = Rs. 6,000 + Rs. 720 - Rs. 500 = Rs. 6,220 - Rs. 500 = Rs. 5720
For the second year, the interest is calculated on the new remaining amount:
Interest = Rs. 5720 × 12% = Rs. (5720 × 0.12) = Rs. 686.40
Again, the instalment of Rs. 500 is paid annually. So, after the second year's payment, the remaining amount to be paid is:
Remaining Amount = Rs. 5720 + Rs. 686.40 - Rs. 500 = Rs. 6236.40 - Rs. 500 = Rs. 5736.40
We can follow the same process for the remaining 10 years:
For the third year: Remaining Amount = Rs. 5736.40 + Rs. 688.37 - Rs. 500 = Rs. 6214.77
For the fourth year: Remaining Amount = Rs. 6214.77 + Rs. 745.77 - Rs. 500 = Rs. 5974.54
...
And so on, until the twelfth year.
Finally, we need to calculate the total amount paid over the 12 years, which is the sum of the cash paid initially and the instalments paid annually:
Total Amount Paid = Cash payment + (12 × Instalment)
Total Amount Paid = Rs. 6,000 + (12 × Rs. 500) = Rs. 6,000 + Rs. 6,000 = Rs. 12,000
Hence, the total cost of the refrigerator after 12 years will be Rs. 12,000.