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Look at this ad:

Buy i-phone 6s plus Now! Pay Later.

Pay 4170 rupees every month, for one year.

Offer is for limited period! Hurry Up!How much money should Ishan pay in one year?

Rayan paid off the bank loan in one year. How much money did he pay the bank?

Remember one method learnt in class 7?Who spent more? How much more?

Ishan was attracted by it and bought a phone from them.

But, Rayan decided to take out a loan from the rural bank for buying the same kind of phone, which Ishan was bought. He made enquiries and found that the actual price of iphone 6s plus was 41700 rupees. He took out a loan from a bank for this amount at 12% interest and bought the phone.

Unseen traps!The colorful ads we see in the papers and TV often do not give full details and real figures.fs

There can be a discussion in class on such hidden facts in ads as well as installment schemes.

Concession in Interest

Remember about Rayans case. He paid off the bank loan of rupees 41700 in one year at 12% interest.Here, Rayan gives interest for 1 year. That is, 41700 1 12/100 = 5004 So, how much does he paid back in 1year? 41700 + 5004 = 46704 rupees.Since it was onam season, the bank offers 2% concession on the interest, if the loan is paid back in half an year. Otherwise there is no concession.After knew about the special offer, Akshaj also took out a loan of same amount and same rate of interest as Rayan took. And he paid all dues on the exact day of completing half an year. How much did he pay back? Amount of loan = 41700 rupees. Rate of interest = 12% Concession = 2% Actual rate of interest = 10% Interest = 41700 10/100 = 2085 rupees. Total amount paid = 41700 + 2085 = 43785 rupees.Who paid more?

See the difference in each case.

Interest for interest

Look at a question:Joseph and Sunny deposit 20,000 rupees each in a bank giving 8% interest annually. After one year, Joseph withdraw the entire amount including interest and re-deposited it the same day. After one more year, both with drew the total amounts. Who got more? How much more?

Have you ever seen such offers in special season?

Buy One! Get One Free!

Sunny gets interest for 2 years. That is, 20000 8/100 2 =3200.So how much does he get in all after two years? 20000 + 3200 = 23200 rupees.

What about Joseph?How much did he get as first years interest? 20000 8/100 = 1600So how much did he withdraw first? 20000 + 1600 = 21600It is the amount that he re-deposited.So how much interest does he get after one more year? 21600 8/100 = 1728What is the total amount? 21600 + 1728 = 23328 rupees.How much more does Joseph get?

The amount he got more is the interest for the first years interest for 20000 rupees.

In many schemes, interest for each year is added to the current amount in calculating interest for the next year, without actual withdrawal and re-investment. Interest calculated thus is called Compound Interest. Interest calculated only on the original investment each year is called Simple Interest.

Look at another problem:

Ram deposited 35000 rupees in a bank which pays 10% interest compounded annually. How much would he get back after two years?

First years amount = 35000 rupees First years interest = 35000 10/100 = 3500 rupees.

Does compound interest mean an interest in compound

Second years amount = 35000+ 3500 = 38500 rupees. Second years interest = 38500 10/100 = 3850 rupees. Amount Ram gets after two years = 35000 + 3850 = 38850 rupees.

Arun deposited 43500 rupees in a bank which gives 8% interest compounded annually. How much would he get after 2 years?Jacob took out an agricultural loan of 13000 rupees from the co-operative bank. They charge 5% interest. How much should Jacob pay back after 6 months?The simple interest at 10% got for a certain amount after a year is 400 rupees. If interest is compound annually, what would be the interest for some amount at the same rate after 3 years?

Computational trick

Activities

Lets see how we can compute the total amount including interest, using algebra. If we denote the current amount by p, the rate of compound interest by r % and compute the total amount including interest to be paid back after n years. Amount for the first year = p Interest for the first year = p r/100 Amount for the second year = p + ( p r/100 ) = P ( 1 + r/100 ) Interest for the second year = p ( 1 + r/100 ) r/100 Interest for the third year = p ( 1 + r/100 ) r/100 r/100 = p ( 1+ r/100 ) + p ( 1 + r/100 ) r/100 = p ( 1+ r/100 ) ( 1 + r/100 ) = p ( 1 + r/100) 2

OMG! Is there any trick to find compo- und interest?

Continuing like this, the total amount A, including interest after n years is given by, A = p ( 1 + r/100 ) n

In general, we can say this:

If p rupees is invested in a scheme giving r % interest compounded annually. The amount got after n years is p ( 1 + r/100 ) n

Now look at this problem:James deposited 10500 rupees in a bank which pays 8% interest compounded annually. How much would she get after 2 years?

By using formula, we can find the amount directly. A = p ( 1 + r/100 ) n So, amount got after 2 years = 10500 ( 1+ 8/100 ) c

= 10500 ( [ 100 + 8 ] 100 ) 2

= 10500 ( 108/100 ) 2

= 10500 ( 1.08 ) 2

= 10500 1.1664

= 12247.2000

= 12247 rupees 20 paisa.

In financial transactions, amounts between 5o paisa and 1 rupee is rounded to 1 rupee and amounts less than 50 paisa are ignored. So, James would get 12247 rupees after 2 years.

108 108 = ( 100 + 8 ) 2

= 10000 + 1600 +64 = 11664 1.08 2 = 1.1664

Compound interest is the 8th wonder of the world He who understands it, earns it He who doesnt pays it - Albert Einstein

Activities

Compute the compound interest for 50050 rupees at 9% for 3 years?Nancy took out a loan of 15000 rupees from a bank, which charges 8% interest compounded annually. She paid back 5000 rupees after 2 years. How much should she pay after one more year to settle the loan?Binny deposited 5000 rupees in a bank, which gives 11% interest compounded annually. After 2 years, he withdraw 3000 rupees. After one more year, how much would she have in her account?

Changing timesThere are several schemes in which interest is calculated every 6 months (half yearly), instead of every year. It is half yearly compounding.

Jincy deposited 36000 rupees in the co-operative bank, which pays interest compound half-yearly. The annual rate of interest is 8%. How much would she get back after one year?

Since interest is compounded half yearly, interest has to be calculated twice a year. Since the interest is 12% each year, it is 6% for 6 months.

Amount for the first 6 months = 36000 rupees Interest for the first 6 months = 36000 6/100 = 2160 rupees. Amount for the next 6 months = 36000 + 2160 = 38160 rupees. Interest for the next 6 months = 38160 6/100 = 2289.6 = 2290 rupees Amount got after 1 year = 38160 + 2290 = 40450 rupees.

Lets look how can we find this by using formula; Amount got after 1 year = 36000 ( 1 + 6/100) 2 = 36000 ( 106/100 ) 2 = 36000 1.06 2 = 40449.6 So, amount got after one year is 40450 rupees.

There are also schemes in which interest is compounded every three month. Such a method is called quarterly compounding.

Suppose Jincy made her deposit in a bank which compounds interest quarterly?

She would get 3% interest every 3 months. So after one year she would get; 36000 ( 1 + 3/100 ) 4 = 36000 (103/100 ) 4 = 36000 1.03 4Compute this with a calculator.

Mohan, Ravi and James deposited 10,000 rupees each, under different schemes, in a bank which gives 8% interest. Mohan gets simple interest, Ravi gets interest compounded half and James gets interest compounded quarterly. Compute the total amount each of them gets back after one year and compare these amounts? Kiran deposited 25,000 rupees in a financial company, which gives 9% interest compounded every six months. How much would he get back after two years?Ravi deposited 30,000 rupees in a bank, which gives 6% interest, compounded quarterly. How much would he get back after 9 months?

Activities

1.03 4 =1.03 21.03 2103 2 = (100 + 3 ) 2

Et Lathika took out a loan of 40,000 rupees from a bank which charges interest compounded quarterly. The annual rate of interest is 8%. How much should she pay back after 9 months to settle the loan?Sujith deposited 15,000 rupees in a bank which compounded interest half yearly and Pranav deposited the same amount in another bank which compounds interest quarterly. The annual rate of interest is 5% at both the banks. How much more would Pranav get after one year?

Increasing and DecreasingThe production of some things increases annually at a fixed rate. Likewise, the price of certain things also increase or decrease at a fixed annual rate. We cam use our method of computing compound interest in such cases also, to calculate the number of units produced each year or the price each year.

Lets look at a related problem.

A company which manufactures computers increases its production by 10% every year. In 2015, the company produced 75,000 computers. How many computers would it produce in 2017?

Here, the number of computers produced every year is 10% more than the number produced the year before.

So, starting with 75000, we have to find the number of computers produced every year after that for two years. Try to find out.

It is the same computation as that of calculating the total amount on compounding interest, isnt?

Look at another problem:

The price of a car is 3 lakh rupees and it depreciates by 4% every year. What would be the price after 2 years?

Here the price on every year is 4% less than the previous years price.

First years price = 3,00,000 First years depreciation = 3,00,000 4/100 = 12,000 rupees. Second years price = 300000 12000 = 2,88,000 Second years depreciation = 288000 4/100 = 11520 Price at the end of two years = 288000 11520 = 276480 rupees.

Here, since the depreciation is at the same rate on every year, we can write

Price at the end of two years = 3,00,000 ( 1 4/100) 2

The population of Kerala increases by 2% in every year. The current population is 3 crores. What would be the population after 3 years?A I.T company reduces the price of a particular model by 4% in every year. The current price of this model is 5000 rupees. What would be the price after 2 years?Tiger is our National Animal. Their number decreases on every year. Figures show 3% annual decrease. According to the census of National Tiger Conservation Authority, there were 1700 tigers in India in 2011. If the trend continues, how many tigers would be there in 2016?

Activities

One problem from Lilavathi, Baskara Charyas book: Oh! Mathematician! If the interest for 100 is 5 per month, say what the interest for 16, for one year is. Then from principal and interest, say what the period is and from period and interest, say what the principal is.

t Project:A report estimates e-waste increasing by 15% every year and the e-waste in 2014 is about 9 crore tons. What is the expected amount of e-waste in 2020?

Collect the details of various schemes for deposits and loans from different banks and compare the rates of interest.

Et

Learning outcomesWhat I canWith teachers helpMust improveExplaining the method of computing interest by compounding interest for interest.Explaining the method of computing amounts under interest compounded, half yearly, quarterly or in any frequencies.Solving other practical problems, using the method of compound interest.

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