Example 1: If Rs. 4000 is invested at 8% p.a. simple interest for 5 years, find the interest.
Sol: simple interest formula: 4000 × 8 × 5/100 = Rs. 1600
Example 2: If Rs 16,000 is invested at 12 percent simple annual interest, how much interest is earned after 6 months?
Sol: Since the annual interest rate is 12 %, the interest for 6 months is (16000x12x6)/12x100 = Rs. 960.
Example 3: A sum was put at simple interest at a certain rate for 6 years. Had it been put at 2 % higher rate, it would have earned Rs 120 more. Find the sum.
Sol: Let P be the principal and x be the original % rate of interest. The interest for 6 years will amount to 6Px/100. If the rate is increased by 2%, the new interest then becomes 6P(x + 2)/100. The difference between the two is c 6P(x + 2)/100 - 6Px/100 = 6P × 2/100.
This is equal to Rs 120. So, P = (120x100)/6x2 = Rs 1000.
Example 4:An amount of Rs. 8000 is lent out in two parts such that the interest on first part at 15 % for 4 years is equal to interest on second part at 4 % for 10 years. Find the sum lent out at 15%.
Sol: Let P be the sum lent out at 15% and Q be the sum lent out at 4%. So Px.15x4 = Qx.04×10
Therefore, P:Q = 15x4/10x4 = 3:2.The total sum of Rs. 8000 is to be divided in the ratio of 3:2. This way the first sum is 8000x3/5 = Rs. 4800.
Example 5: Shamrao deposits Rs 2,000 in his savings account at Bank of Maharashtra at 4% and Rs 3,000 in US – 64 at 14% p.a. Find the rate of interest for the whole sum.
Sol: Shamrao earns an interest of Rs 0.04 x 2000 = Rs. 80 in the Bank of Maharashtra account.
He earns an interest of Rs. 0.14 3000 = Rs. 420 in US – 64.Total interest income = 80 + 420 = 500.
→Total principal = Rs. 5000. So, the rate on total amount = 100 × 500/5000 = 10 %.
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Example 6: A Sum of money at simple interest of 20% p.a. will take how many years to double itself?
Let the Principal be Rs. 100. The amount after the specified time = Rs. 200.
Therefore, Interest = Amount – Principal = Rs. 200 – Rs. 100 = Rs. 100. Rate = 20%.
Using the formula S.I. × 100 = P × R × T and putting the values in this formula, we get
100 × 100 = 100 × 20 × T → T = 5 years.
- Sometimes instead of interest, the amount is given, then either you add the above simple interest formula in the principal again and then solve the equation or apply the following straight formula.
Example 7: What sum of money amounts to Rs. 3900 in 2 years at 15% p.a. Simple Interest?
Using the formula
and putting the values, we get
Principal = 3900x100/100+(15x2) = 3900x100/130 = 3000
Hence, Principal = Rs. 3000.
- Sometimes, the amount is given, but instead of principal, the simple interest is asked in the question which can be calculated with the help of the following straight formula
The above-mentioned principal is also called ‘present worth’ of the amount. Similarly, the simple interest is also called ‘true discount’ on the amount.
Example 8: A sum of money amounts to Rs. 9600 in 2 years at 10% p.a. Find the simple interest.
Using the formula,
and putting the values, we get
Simple Interest = 9600x10+2/100+(10x2) = 9600x10x2/120 = 1600
Example 9: A certain sum of money amounts to Rs. 630 in 2 years and to Rs. 675 in 5 years. Find the sum and the rate of interest.
Sol: P + (S.I. for 5 years) = Rs. 675 and P + (S.I. for 2 years) = Rs. 630.
On subtracting, S.I. for 3 years = Rs. 675 – Rs. 630 = Rs. 45. therefore, S.I. for 1 year = Rs. 45/3 = Rs. 15
therefore, S.I for 2 years = Rs. 15 × 2 = Rs. 30. therefore, P = Rs. 630 – Rs. 30 = Rs. 600.
Using the formula S.I. × 100 = P × R × T and putting the values in this formula, you get 30 × 100 = 600 × 2 × R → R = 2.5% p.a.
Example 10: What annual installment will discharge a loan of Rs. 5900, due after 5 years, the rate of interest being 9 % per annum?
The first error, the student can make in this case, is if she treats Rs. 5900 as the principal. The following method should be applied to solve this kind of question.
The first installment will be paid one year from now i.e. 4 years before it is due.
The second installment will be paid two years from now i.e. 3 years before it is due.
The third installment will be paid 2 years before it is due.
The fourth installment will be paid 1 year before it is due.
The fifth installment will be paid on the day the amount is due.
So, on the first installment, the interest will be paid for 4 years, on the second for 3 years, on the third for 2
years, on the fourth for 1 year and on the fifth for 0 year.
In total, an interest for 10 years will be paid (4 + 3 + 2 + 1 + 0) on Rs. 100 @ 9 %.
Interest = 100x10x9/100 = Rs. 90 and the principal is Rs 100 × 5 = Rs. 500.
The total loan that can be discharged is Rs. 500 + 90 = Rs. 590.
Here, Chain Rule will be applied. i.e. for Rs. 590 the installment required is Rs. 100, for Rs. 5900 the installment required is 5900 × 100/590 = Rs. 1000.
Otherwise the following straight method can also be applied, where the annual installment required is equal to =