## Monday, November 09, 2015

### Installment Concept of Simple and Compound Interest, Compounding More than once in an year, Current Value of an Amount

First of all this video is an attempt towards a very short revision of what has been already completed by me by explaining or to be precise revising the below four statements for you.
Statement 1. If Compounding of Interest is done more than once in an year say n times so we can conclude that the compounding is done after every (12/n) months and we suppose the rate of Interest to be R % per annum then the after t years, any principal P will increase to an amount A = P(1 + (R/100n))nt

Statement 2. Whenever any situation like above arises where compounding is being done more than once in a year, then the rate of interest given in any problem will be termed as Nominal Rate of Interest. So R % in the above question becomes the nominal rate of Interest and whenever we are going to express the interest obtained above in terms of a rate obtained at simple interest than that rate will be termed as Effective Rate of Interest.

Statement 3. The difference between the Compound Interest and Simple Interest on a certain sum for two years in equal to the interest calculated for one year on one year's Simple Interest. This means that the difference would become P(R/100)(R/100) = PR2/1002

Statement 4. The difference between the Compound Interest or Amount for t years and (t+1) years is the interest on one year Compound Interest for the tth year or on the amount at the end of t years respectively. This can also be said as that the difference between the Compound Interest for the tth year and (t+1)th year is equal to the interest for one year on the compound interest for the tth year.

Questions relating to these concepts have been taken by me with proper solution in the video.

After that I have told you the concept of current value or present value of an installment which is very important to understand in order to have a grasp over the concept of both Simple Interest installment and Compound Interest Installment.

Then I have explained the formula of calculating the installment levied in case of Simple Interest and after that I had done the same for Compound Interest. Formula for both of these installments have been proved by me in this video. It is upto to you whether you would like to directly use the formula or would solve the question using the formula deriving method.

The questions discussed by me in this video are -

Question 1. The compound interest on a certain sum at a certain rate of interest for the second year is Rs. 2200 and for the third year is Rs. 2420. Find the Principal and Rate of Interest ??

Question 2. Find the current/present value of the payments received if Compound Interest at 10 % per annum is charged. Rs. 7700 are received at the end of first year and Rs. 7623 at the end of second year.

Question 3. Arun makes an investment of Rs. 20000 with the HDFC Investment group. If the rate of interest be 13 % Simple Interest per annum charged half yearly, what amount will he get after 42 months ??

Question 4. Sanjay makes a deposit of Rs. 1,00,000 in Axis Bank for a period of 2 years. If the rate of interest be 12 % per annum compounded half yearly, what amount will he get after 2 years ??

Question 5. What annual installment will discharge a debt of Rs. 4200 due in five years at 10 % Simple Interest ?

Question 6. A sum of Rs. 2 is lent to be paid back in 3 equal monthly installments of Rs. 1 each. Find the rate of interest ??

Question 7. What quarterly payment will discharge a debt of Rs. 2280 due in 2 years at 16 % Simple Interest ?

Question 8. A person borrowed a sum of Rs. 6600 at 10 % per annum interest compounded annually. If the money is to be repaid in three equal annual installment, each payable at the end of the year, then what is the value of each installment ??

Question 9. Three equal installment, each of Rs. 200 were paid at the end of year on a sum borrowed at 20 % compound interest, compounded annually. Find the sum.

Question 10. A man borrows a certain sum of money and pays it back in two years in two equal installments. If compound interest is charged at 5 % per annum and he pays back annually Rs. 441, what sum did he borrow ??

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