Class 8 RD Sharma Solutions Chapter 14 Compound Interest Exercise 14.5 (original) (raw)
Last Updated : 23 Jul, 2025
**Question 1. Ms. Cherian purchases a boat for Rs. 16000. If the total cost of the boat is depreciating at the rate of 5% per annum, calculate its value after 2 years.
**Solution:
We have,
Price of a boat is = Rs 16000
Depreciation rate = 5% per annum
By using the formula,
A = P (1 + R/100)t
Substituting the values, we have
= P (1 + R/100)2
Since it is depreciation we use P (1 – R/100)n
= 16000 (1 – 5/100) (1 – 5/100)
= 16000 (95/100) (95/100)
= 16000 (0.95) (0.95)
= 14440
Therefore,
Value of the boat after two years is Rs 14440.
**Question 2. The value of a machine depreciates at the rate of 10% per annum. What will be its value 2 years hence, if the present value is Rs 100000? Also, find the total depreciation during this period.
**Solution:
We have,
Present value of machine is = Rs 100000
Rate of depreciation = 10% per annum
By using the formula,
A = P (1 + R/100)t
Substituting the values, we have
= 100000 (1 – 10/100) (1 – 10/100)
= 100000 (90/100) (90/100)
= 100000 (0.9) (0.9)
= 81000
Value of machine after two years will be Rs 81000
Therefore,
Total depreciation during this period is Rs (100000 – 81000) = Rs 19000.
**Question 3. Pritam bought a plot of land for Rs. 640000. Its value is increasing by 5% of its previous value after every six months. What will be the value of the plot after 2 years?
**Solution:
We have,
Price of land is = Rs 640000
Rate of increase = 5% in every six month
By using the formula,
A = P (1 + R/100)t
Substituting the values, we have
= 640000 (1 + 5/100) (1 + 5/100) (1 + 5/100) (1 + 5/100)
= 640000 (105/100) (105/100) (105/100) (105/100)
= 640000 (1.025) (1.025) (1.025) (1.025)
= 706440.25
Therefore,
The value of the plot after two years will be Rs 706440.25.
**Question 4. Mohan purchased a house for Rs. 30000 and its value is depreciating at the rate of 25% per year. Find the value of the house after 3 years.
**Solution:
We have,
Price of house is = Rs 30000
Depreciation rate is = 25% per year
By using the formula,
A = P (1 + R/100)t
Substituting the values, we have
= 30000 (1 – 25/100) (1- 25/100) (1 – 25/100)
= 30000 (75/100) (75/100) (75/100)
= 30000 (0.75) (0.75) (0.75)
= 12656.25
Therefore,
The value of the house after 3 years is Rs 12656.25
**Question 5. The value of a machine depreciates at the rate of 10% per annum. It was purchased 3 years ago. If its present value is Rs. 43740, find its purchase price.
**Solution:
We have,
Present value of machine is = Rs 43740
Depreciation rate of machine is = 10% per annum
Let the purchase price 3 years ago be = Rs x
By using the formula,
A = P (1 + R/100)t
Substituting the values, we have
43740 = x (1 – 10/100) (1 – 10/100) (1 – 10/100)
43740 = x (90/100) (90/100) (90/100)
43740 = x (0.9) (0.9) (0.9)
43740 = 0.729x
x = 43740/0.729
= 60000
Therefore,
The purchase price is Rs 60000.
**Question 6. The value of a refrigerator which was purchased 2 years ago, depreciates at 12% per annum. If its present value is Rs. 9680, for how much was it purchased?
**Solution:
We have,
Present value of refrigerator is = Rs 9680
Depreciation rate is = 12%
Let the price of refrigerator 2 years ago be = Rs x
By using the formula,
A = P (1 + R/100)t
Substituting the values, we have
9680 = x (1 – 12/100) (1 – 12/100)
9680 = x (88/100) (88/100)
9680 = x (0.88) (0.88)
9680 = 0.7744x
x = 9680/0.7744
= 12500
Therefore,
The refrigerator was purchased for Rs 12500.
**Question 7. The cost of a T.V. set was quoted Rs. 17000 at the beginning of 1999. In the beginning of 2000 the price was hiked by 5%. Because of decrease in demand the cost was reduced by 4% in the beginning of 2001. What was the cost of the T.V. set in 2001?
**Solution:
We have,
Cost of T.V at beginning of 1999 is = Rs 17000
Hiked in price in the year 2000 is = 5%
Depreciation rate in the year 2001 is = 4%
By using the formula,
A = P (1 + R/100)t
Substituting the values, we have
= 17000 (1 + 5/100) (1 – 4/100)
= 17000 (105/100) (96/100)
= 17000 (1.05) (0.96)
= 17136
Therefore,
The cost of TV set in the year 2001 is Rs 17136.
**Question 8. Ashish started the business with an initial investment of Rs. 500000. In the first year he incurred a loss of 4%. However during the second year he earned a profit of 5% which in third year rose to 10%. Calculate the net profit for the entire period of 3 years.
**Solution:
We have,
Initial investment by Ashish is = Rs 500000
Incurred loss in the first year is = 4%
Profit in 2nd year is = 5 %
Profit in 3rd year is = 10%
By using the formula,
A = P (1 + R/100)t
Substituting the values, we have
= 500000 (1 – 4/100) (1 + 5/100) (1 + 10/100)
= 500000 (96/100) (105/100) (110/100)
= 500000 (0.96) (1.05) (1.1)
= 554400
Therefore,
The net profit for the entire period of 3 years is Rs 554400.
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Unsolved Practice Problems
- **A car is purchased for Rs. 250000. If its value depreciates at the rate of 8% per annum, calculate its value after 3 years.
- **A laptop costs Rs. 50000 and its value decreases by 6% per year. What will be its value after 4 years?
- **If a watch worth Rs. 12000 depreciates at a rate of 7% per annum, what will be its value after 5 years?
- **A property bought for Rs. 800000 depreciates by 10% every year. Find its value after 2 years.
- **A piece of equipment costs Rs. 150000 and depreciates at 15% annually. What will be its value after 3 years?
- **The initial cost of a machine is Rs. 90000 and it depreciates at a rate of 12% per year. Determine the machine's value after 2 years.
- **If the value of an office desk decreases by 4% each year, what is its value after 3 years if it was originally purchased for Rs. 20000?
- **A printer bought for Rs. 30000 depreciates by 5% every 6 months. What will be its value after 1 year?
- **The cost of a bicycle is Rs. 10000 and it depreciates at 8% per annum. Find its value after 2 years.
- **A television set is bought for Rs. 40000 and depreciates at 9% per annum. Calculate its value after 3 years.