Before going to the simple interest and compound interest problems, you should revise the simple and compound interest formulas. After revising the formulas you will understand the following examples.
Example 1:If the difference between Simple Interest and Compound Interest on a certain sum of money in 2 years at 20 % p.a. is Rs. 800, then find the sum.
Sol:If difference between Simple Interest & Compound Interest for 2 years is Rs. x, then Principal = x
(100/r)2 P = 800 X 10000/20*20 → P = 20000. Hence the sum is Rs. 20000.
Example 2:The compound interest on a certain sum of money for 2 years is Rs. 52 and the simple interest for the same time at the same rate is Rs. 50. Find the rate %.
Sol:SI for 2 years = 50, CI for 2 years = 52. therefore As, SI and CI are same for the first year,
therefore, SI and CI for 1st year = Rs. 25. So CI for 2nd year = 52 – 25 = 27
i.e. a difference of Rs. 2 on 1st year’s interest of Rs. 25. Hence rate of interest = 100 X 2/25 = 8%.
Example 3:The difference between Compound Interest and Simple Interest on a certain sum of money at 10 % per annum for 3 years is Rs. 930. Find the principal if it is known that the interest is compounded annually.
Sol: The Simple Interest after three years @ 10% is 30%.
The Compound Interest after 3 years @ 10% will be 1.1 × 1.1 × 1.1 = 1.331 Cumulative rate of Interest is 33.1%.
Here, the difference after 3 years is 3.1% and in the question it is given to be Rs. 930.
Thus, the Principal is 930 × 100/3.1 = Rs. 30000.
Example 4:The population of a town has a constant growth of 4% p.a. If its present population is 62,500, what will be its population after two years?
Sol:: Population after 2 years = P (1 + 4/100)2 = 62500 X (104/100)2
= 62500 × 26/25 X 26/25 = 100 × 26 ×26 = 67600.
Hence, the population after two years will be 67,600.
Example 5:The cost of a new washing machine is Rs. 12000. Its value depreciates every year at the rate of 10%. What will be its value after three years?
Sol:The cost of washing machine = Rs. 12000
Rate of depreciation = 10%, Time = 3 years
Due to depreciation, the price of the washing machine is reduced.
Therefore, Price of washing machine after three years
= Rs. 12000 × (1 - 10/100)3 = Rs. 12000 × (90/100)3 = Rs. 12000 × 9/10 x 9/10 x 9/10 = Rs. 8748.