Anjali took a loan of Rs. 20,000 to purchase a TV set from LG. She pro...
Given:
Anjali took a loan of Rs. 20,000 to purchase a TV set from LG. She promised to make the payment after three years. The company charges Compound Interest (CI) at a rate of 10% per annum for the first two years. However, the company suddenly announces a rate of interest of 15% per annum for the last one year of the loan period.
To find:
The extra amount Anjali has to pay due to the announcement of the new rate of interest.
Solution:
To solve this problem, we need to calculate the interest amount for two different periods - the first two years at a rate of 10% and the last one year at a rate of 15%.
Calculating the interest for the first two years:
Given that the loan amount is Rs. 20,000 and the rate of interest is 10% per annum.
Using the formula for Compound Interest: A = P*(1 + R/100)^T
Where,
A = Amount after interest
P = Principal amount (loan amount)
R = Rate of interest
T = Time period in years
Substituting the values into the formula, we get:
A = 20,000 * (1 + 10/100)^2
= 20,000 * (1 + 0.1)^2
= 20,000 * (1.1)^2
= 20,000 * 1.21
= 24,200
Therefore, the amount after two years is Rs. 24,200.
Calculating the interest for the last one year:
Given that the loan amount is Rs. 24,200 (amount after two years) and the rate of interest is 15% per annum.
Using the same formula for Compound Interest, we get:
A = 24,200 * (1 + 15/100)^1
= 24,200 * (1 + 0.15)^1
= 24,200 * (1.15)^1
= 24,200 * 1.15
= 27,830
Therefore, the amount after the last year is Rs. 27,830.
Calculating the extra amount:
The extra amount Anjali has to pay due to the announcement of the new rate of interest can be found by subtracting the loan amount from the final amount after three years.
Extra amount = Final amount - Loan amount
= Rs. 27,830 - Rs. 20,000
= Rs. 7,830
Therefore, Anjali has to pay an extra amount of Rs. 7,830 due to the announcement of the new rate of interest.
Conclusion:
The extra amount she has to pay due to the announcement of the new rate of interest is Rs. 7,830.