Sales Toll Free No: 1-855-666-7440
Compound Interest
When interest is Compounded Annually but Rates being Different for Different years.
Supposed Principal = Rs P, Time = 2 Years and rates of interest be a% and b% for year and second year respectively.
Then, amount after 2 years = Rs [P(1+ a/100) (1 + b/100)]
This formula may similarly be extended for any number of years.
Example:- Find the amount of Rs 16500 for 2 years compounded annually, the rate of interest being
10% for first year and 12% for the second year
Solution.
Here, P = Rs 16500, a = 10% p.a. and b = 12% p.a.
.^{.}. Amount after 2 years = P (1 +a/100) (1 + b/100)
= Rs [16500 × (1 + 10/100) × (1 + 12/100)]
= Rs (16500 × 11/10 × 28/25) = Rs 20328
When interest is Compounded Annually, but Time being a Fraction, say 2,3/5 Years.
In this case,
Amount = P(1 + R/100)^{2} (1 + 3/5 × R/100)
Example:- Find the compound interest on Rs 16000 at 15% per annum 2,1/3 years.
Solution.
Amount after 2,1/3 years
= Rs[16000 × (1 + 15/100)^{2} × (1 + 1/3× 15/100)]
= Rs(16000 × 23/20 × 23/20 × 21/20) = Rs 22218
.^{.}. Compound Interest = Rs (22218 – 16000) = Rs 6218
1. Find the amount of Rs 6250 at 8% per annum compound interest for 2 years. Also, calculate the
compound interest?
2. Calculate the compound interest on Rs 14500 at 10% per annum for 3 years/
3. Mohan Lal took a loan of Rs 25600 from a bank to renovate his house. If the rate of interest be
13,3/4% per annum, find the compound interest, he will pay after 2years?
4. A farmer obtained a loan of Rs 12800 from Vijaya bank for buying a tractor. If the bank charges
compound interest at 7,1/2% per annum, what amount he will have to pay after 3 years?
INTRODUCTION
A shopkeeper buys goods either form a factory or through a wholesaler. He then sells these articles to his customers.
Usually, a shopkeeper sells an article at a price higher than the price at which he buys it. In such cases, he makes a profit or gain.
Example:- Suppose a shopkeeper buys a umbrella for Rs 200 and sells it for Rs 250. Clearly, he has a profit of Rs 50 in this transaction.
Sometimes, the items purchased by a shopkeeper are defective or they become outdated. In such circumstances, he is forced to sell them even at a price lower than the price at which they are purchased. In such eases, the shopkeeper suffers a loss.
Example:- Suppose a shopkeeper buys a pair of socks for Rs 25 and sells it for Rs 20. Clearly, he has a loss of Rs 5 in this transaction.
Cost Price
The price at which an article is purchased is called its cost price. In short, we write it as C.P.
Selling Price
The price at which an article is sold is called its selling price. In short, we write it as S.P.
Profit or Gain
If S.P. is more than the C.P., then the seller has a profit or gain
Profit = (S.P.) – (C.P.)
Loss
If S.P. is less than the C.P., then the seller incurs a loss
Loss = (C.P.) – (S.P)
Profit or Loss is Always Calculated on C.P.
Profit on Rs 100 is called Profit %
Profit % = (Profit/C.P. × 100) % |
Loss on Rs 100 is called Loss %
(i) When an article is sold at r% gain, then:
S.P. = (100 + r) % of C.P.
S.P. (100 + r/100) × C.P. |
(ii) When an article is sold at r% loss, then:
S.P. = (100 – r) % of C.P.
S.P. (100 – r/100) × C.P. |
From the above two results, we get:
(iii)
C.P. 100/ (100 + r) × S.P., in case of r % gain. |
(iv)
C.P. 100/(100 – r) S.P., in case of r % loss |
Remark.
(i) If an article is sold at a gain of 25%, then S.P. = 125% of C.P.
(ii) If an article is sold at a loss of 20%, then S.P. = 80% of C.P.
The total profit (income) without deducting tax is called gross profit (income).
Net Profit (Income)
The profit (income) after deducting tax is called net profit (income)
Note:- When C.P. and S.P. are given for different number of articles, we find the C.P. as well as S.P.
of an equal number of articles (usually, one) and then calculate profit or loss.
Sometimes, apart form paying the cost of an article, a shopkeeper has to spend money on transportation, labour, repair, etc. Such expenses are known as overhead expenses.
Actual C.P. of an article = Cost of the article + Overhead Expenses
Example1. A man buys an article for Rs 78 and sells it for Rs 89.70. Find his profit his profit per cent.
Solution
C.P. = Rs 78, S.P. = Rs 89.70
.^{.}. Profit = (S.P.) – (C.P.)
= Rs (89.70 – 78) = Rs 11.70
.^{.}. Profit % = (11.70/78 × 100) % = 15%
Example2. A watch is bought Rs 875 and sold for Rs 717.50. Find the lose per cent.
Solution.
C.P. = Rs 875, S.P. = Rs 717.50
.^{.}. Loss = (C.P.) – (S.P.)
= Rs (875 – 171.50) = Rs 157.50
.^{.}. Loss % = (157.50/875 × 100) % = 18%
Example3. A T.V. and a VCR were sold for Rs 19800 each. The TV was sold at a loss of 10% whereas the VCR at a gain of 10%. Find the gain or loss per cent in the whole transaction.
Solution.
S.P. of TV = Rs 19800, Loss % = 10%
.^{.}. C.P. = 100/(100 – r) × S.P., where r = 10
= [(100/(100 – 10) × 19800] = Rs (100/90 × 19800) = Rs 22000
S.P. of VCR = Rs19800, Gain % = 10%
.^{.}. C.P. = 100/(100 + r) × S.P., where r = 10
= Rs[100/(100 + 10) × 19800] = (100/110 × 19800) = Rs 18000
Total C.P. of TV ad VCR = Rs (22000 + 18000) = Rs 40000
Total S.P. of TV and VCR = Rs(2 × 19800) = Rs 39600
.^{.}. Loss = (C.P.) – (S.P.)
= Rs (40000 – 39600) = Rs 400
Loss % = (400/40000 × 100) % = 1%
Hence, there was a loss of 1% in the whole transaction.
1. Find the profit or loss per cent, when:
(i) C.P. = Rs 55 and S.P. = Rs 72.60
(ii) C.P. = Rs 490 and S.P. = Rs 416.50
(iii) C.P. = Rs 112, overheads = Rs 14 and S.P. = Rs 94.50
2. Find S.P. when:
(i) C.P. = Rs 435 and loss = 16%
(ii) C.P. = Rs 172, overheads = Rs 61 and gain = 12%
3. A man sells an article at a profit of 25%. If he had bought it at 20% less ad sold it for Rs 10.50 less,
he would have gained 30%. Find the cost price of the article?
4. 20% more can be gained if a piece of cloth is sold for Rs 83 instead of Rs 78. Find the cost price of
the piece of cloth?