# ACCOUNTING & FINANCE FOR BANKERS EBOOK

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JAIIB-MACMILLAN EBOOK-Principles and Practices of sppn.info . Principles & Practices of Banking 2. Accounting & Finance for Bankers 3. eBook - INFORMATION TECHNOLOGY. eBook - ADVANCED BANK MANAGEMENT. eBook - BANK FINANCIAL MANAGEMENT. eBook - ACCOUNTING. JAIIB MADE EASY 2: ACCOUNTING & FINANCE FOR BANKERS – A COMPLETE BOOK: Updated specially for exam eBook: EXPERIENCED.

## JAIIB-MACMILLAN eBook-Accounting and Finance for Bankers

Therefore, there is a need for today's bank employees to keep themselves updated with a new set of skills and knowledge. The Institute, being the main provider of banking education, reviews the syllabus for its associate examinations, viz. The latest revision has been done by an expert group under the Chairmanship of Prof. Candidates to the course will get extensive and detailed knowledge on banking and finance and details of banking operations. The Diploma is offered in the distance learning mode with a mix of educational support services like provision of study kits, contact classes, etc.

The key features of the Diploma is that it aims at exposing students to real-life banking environment and that it is equivalent to JAIIB. Marketing of Bank products have been covered in length.

Aspects such as insurance, mutual funds, credit cards, etc. The flow of transactions in a centralised computerised operating environment and delivery of services through multiple channels have been given adequate coverage to make the participants aware of the latest banking environment and practices. The Institute acknowledges with gratitude the valuable services rendered by the authors in preparing the courseware in a short period of time.

However, the candidates could still refer to a few standard textbooks to supplement this material which we are sure, will enhance the professional competence of the candidates to still a higher degree. We have no doubt that the study material will be found useful and will meet the needs of the candidates to prepare adequately for the examinations. We welcome suggestions for improvement of the book. Mumbai R. The candidates would be able to acquire an in-depth knowledge of the following: Traits Rubrics Jul 23, Balance Sheet Equation Partnership Accounts Final Accounts of Banking Companies Company Accounts - I Company Accounts - II Accounting in Computerised Environment Calculation of Interest Unit 2.

Calculation of YTM Unit 4. Capital Budgeting Unit 5. Depreciation Unit 6.

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Foreign Exchange Arithmetic. The objectives of the unit are to understand: Banking business mainly consists of lending. On lending to customers, the bank charges a certain interest at a specified rate. The interest is payable either at periodic intervals or at the end of a loan period. The calculation of the interest will be based on the terms of agreement, i.

Sometimes, it also happens that the customer is interested in paying a part of principal along with interest. As the customers pay the principal in instalments, the impact of the interest gets reduced over the tenure of loan. It may also happen that the bank may want to recover the loan in equal instalments called annuities. Annuities are essentially a series of fixed payments required to be paid at a specified frequency over the course of a fixed period of time.

Payment of annuities may be at the beginning of each period or at the end of each period. The calculations of annuities are different for each situation.

Sometimes, the bank also needs to make a cost-benefit analysis of the series of annuities and is required to calculate the present value of all the annuities by suitably discounting the annuities receivable at the end of each period.

The sums of the present value of the annuities are compared with the cash outflow to reach certain decisions. When money is loaned, the borrower usually pays a fee to the lender. This fee is called 'interest'. Based on the method of calculation of the amount of interest given on the amount lent or borrowed, the interest can be simple interest or compound interest.

The formula for calculating simple interest is as follows: The rate is expressed as a decimal fraction, so must divide percentages.

The formula for simple interest is often abbreviated in this form: Three other variations of this formula are used to find the P, R and T. The Illustration problem below shows you how to use these formulas: Illustration A student downloads a computer by obtaining a loan on simple interest. The computer costs Rs. If, the loan is to be paid back in weekly instalments over two years, calculate: The amount of interest paid over the two years, 2. The total amount to be paid back, 3.

The weekly payment amount. Find the amount of interest paid.

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Find the total amount to be paid back. In the simple interest formula, it is presumed that interest is charged only once during the given period. Against this, if the interest is charged more than once during the period and the interest is reinvested, we need to compound the interest.

Compound interest is paid on the original principal and accumulated part of interest. However, when interest is added to the account versus returning it immediately to the customer, the interest itself will earn interest during the next time for computing the interest.

This is compounding interest or more simply stated compound interest. The time interval between which the interest is added to the account is called the compounding period.

The interest rate together with compound period and balance in the account determines how much interest is added to each compound period. The above is more easily understandable by thinking in terms of a simplified compound interest. As you can see, there is an advantage to compounding more frequently. If the balancing interest rate and length of the deposit all remain the same, more interest is earned by increasing the compounding periods per year.

Special Note: The Rule of Allows you to determine the number of years before your money doubles whether in debt or investment. Here is how to do it; Divide the number 72 by the percentage rate you are paying on your debt or earning on your investment. For an illustration: You borrowed Rs. Then, 72 divided by 6 is That makes 12 the number of years it would take for your debt to double to Rs.

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Similarly, a saving account with Rs. Simple interest questions can be solved by applying the following formulas: Illustration Mohan invested Rs.

How much interest would he earn after 2 years? Illustration Jhangir has one savings account with the interest rate of 3. If he deposits Rs. Answer Savings account: Illustration Your friend borrows Rs. She expects to be able to pay you back the Rs. She will owe you Rs. Illustration Your friend expects to pay you the principal back after she files her tax return, but you would like to receive the interest monthly. The extra step here is that the interest rate of 8 per cent is the annual rate and this needs to be divided by 12 to get a monthly rate.

Because the principal amount remained the same for each month, the calculation in either way will get the same result. Our first two illustrations for calculating of simple interest assumed the principal amount remained the same for the entire period the loan was outstanding.

In the real world, it is not usually the way consumer loans are done. Most of us receive payment on a regular basis, say every two weeks or perhaps monthly, so it makes more sense to match the repayment of the loans to the way we are paid.

Here is what happens with monthly payments and simple interest: Illustration Your friend wants to repay you on a monthly basis rather than the whole amount all at once at the end of the year. The extra step here is that she will owe you less in principal each month. This is where it starts to get complicated, but the formula is the same. We just have to do it 12 times. The principal payment each month will be Rs. The principal owed at the end of the month is Rs. Second month: Third month: And so on for the twelve months.

Easy to see why calculators and computers are used, right? Table 1. Illustration Your friend says, 'look, I want to pay the same amount every month and not have to look up this table. Add up the twelve monthly payments Rs. Under this system, the principal and the interest thereon is repaid through equal monthly installment over the fixed tenure of the loan.

The EMI is fixed based on the loan amount, interest rate and the repayment tenure. The formula for calculation of EMI given the loan, term and interest rate is:.

Though it is an unequal combination of the principal repayment and interest cost, it remains constant all through. The interest is calculated on a monthly reducing basis, which means that the principal amount you pay every month is deducted when calculating the interest for the following months.

Therefore, for a payment made on 15 January, the interest rate adjustment takes effect from the next month. The EMI payment loans are heavily tilted towards the interest payments at the start and principal repayments towards the end of the loan tenure. For example, the appropriation towards the interest and principle out of the EMI payments based on the above given example is given below assuming that the loan is taken on 15th January, There are two different modes of interest.

They are 1. Fixed Rates 2. Floating Rates also called as variable rates. Fixed Rate: In the fixed rate, the rate of interest is fixed. It will not change during entire period of the loan. For example, if a home loan, taken at an interest rate of 12 per cent, is repayable in 10 years, the rate will remain the same during the entire tenure of 10 years even if the market rate increases or decreases. The fixed rate is, normally, higher than floating rate, as it is not affected by market fluctuations.

Floating Rate: In the floating rate or variable rate, the rate of interest changes, depending upon the market conditions.

It may increase or decrease. For example, if a home loan is taken at an interest rate of 12 per cent, repayable in 10 years, in April , and if the market rate increases to If the loan is under an EMI system, depending upon the change in interest rate, the repayment period varies, but equated monthly instalment remains the same.

Depending on the prevailing market conditions, people may choose between the fixed rate and a floating rate. At some point in your life, you may have had to make a series of fixed payments over a period of time - such as rent or car payments - or have received a series of payments over a period of time, such as bond coupons.

These are called annuities. If you understand the time value of money and have an understanding of the future and present value, it would be easy to understand annuities. Annuities are essentially a series of fixed payments required from you or paid to you at a specified frequency over the course of a fixed period.

The most common payment frequencies are yearly once a year , semi-annually twice a year , quarterly four times a year , and monthly once a month. There are two basic types of annuities: Ordinary Annuity: Payments are required at the end of each period. For an illustration, straight bonds usually make coupon payments at the end of every six months until the bond's maturity date. Annuity Due: Payments are required at the beginning of each period.

Rent is an illustration of annuity due. You are usually required to pay rent when you first move in at the beginning of the month, and then on the first of each month thereafter. Since the present and future value calculations for ordinary annuities and annui ties due are slightly www. If you know how much you can invest per period for a certain time period, the future value of an ordinary annuity formula is useful for finding out how much you would have in the future by investing at your given interest rate.

If you are making payments on a loan, the future value is useful for determining the total cost of the loan. Let us now run through the illustration 1. Consider the following annuity cash flow schedule:. In order to calculate the future value of the annuity, we have to calculate the future value of each cash flow. Let us assume that you are receiving Rs.

The following diagram shows how much you would have at the end of the five-year period:.

## Principles & Practices of Banking

I I I I Payment paid or received at end of each period. Since, we have to add the future value of each payment, you may have noticed that, if you have an ordinary annuity with many cash flows, it would take a long time to calculate all the future values and then add them together. Fortunately, mathematics provides a formula that serves as a short cut for finding the accumulated value of all cash flows received from an ordinary annuity:.

Each of the values of the first calculation must be rounded to the nearest paise. The more you have to round numbers in a calculation the more likely rounding errors will occur. Therefore, the above formula not only provides a short cut to finding FV of an ordinary annuity but also gives a more accurate result. If you would like to determine today's value of a series of future payments, you need to use the formula that calculates the present value of an ordinary annuity.

You would use this formula as part of a bond pricing calculation. The PV of ordinary annuity calculates the present value of the coupon payments that you will receive in the future. For the illustration 2, we will use the same annuity cash flow schedule as we did in the illustration 1. To obtain the total discounted value, we need to take the present value of each future payment and, as we did in the illustration 1, add the cash flows together. End of each period.

Again, calculating and adding all these values will take a considerable amount of time, especially if we expect many future payments. As such, we can use a mathematical shortcut for PV of ordinary annuity. Cash flow per period www. Here is the calculation of the annuity represented in the diagram for Illustration 2: Beginning of each period.

Payment paid or received at the beginning of each period. Since, each payment in the series is made one period sooner; we need to discount the formula one period later. A slight modification to the FV-of-an-ordinary-annuity formula accounts for payments occurring at the beginning of each period. In the following Illustration 3, let's illustrate why this modification is needed when each Rs. Notice that when payments are made at the beginning of the period, each amount is held for longer than at the end of the period.

For example, if Rs. The future value of annuity formula would then read:. For the present value of an annuity due, we need to discount the formula one period forward, as the payments are held for a lesser amount of time.

When calculating the present value, we assume that the first payment made was today. We could use this formula for calculating the present value of your future rent payments as specified in a lease you sign with your landlord. Let us say for the illustration that you make your first rent payment at the beginning of the month and are evaluating the present value of your five-month lease on that same day. Your present value calculation would work as follows:. Therefore, 1.

The present value of an ordinary annuity is less than that of an annuity due because the further back we discount a future payment, the lower is its present value: Now you can see how annuity affects and how you calculate the present and future value of any amount of money. Remember that the payment frequencies, or number of payments, and the time at which these payments are made whether at the beginning or end of each payment period , are all variables you need to account for in your calculations.

Illustration Find the compound amount of Rs. Solution Using formula, we could find the value of compound amount. However, in these kinds of problems, generally we use compound interest for the full interest period and simple interest for the fractional interest period.

Here we find the compound interest for 13 interest periods and simple interest for 1 month. Find i the rate of interest, ii the principal, iii the difference between the C. Solution i Let the principal be Rs.

P and rate of interest be R per centp.

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If the present population is 1 million, estimate the population five years hence. Also, estimate the population three years ago.

Illustration Avichal Publishers download a machine for Rs. The rate of depreciation is 10 per cent. Find the depreciated value of the machine after 3 years. Also, find the amount of depreciation. What is the average rate of depreciation? In this chapter, we shall discuss different methods of repaying interest-bearing loans, which is one of the most important applications of annuities in business transactions. The first and most common method is the amortisation method.

By using this method to liquidate an interest-bearing debt, a series of periodic payments, usually equal, are made. Each payment pays the interest on the unpaid balance and repays a part of the outstanding principal.

As time goes on, the outstanding principal is gradually reduced and interest on the unpaid balance decreases. When a debt amortises, by equal payments at equal payment intervals, the debt becomes the discounted value of an annuity.

The common commercial practice is to round the payment up to the next rupee. Thus, an annuity is a sequence of payments made at regular periods over a given time interval e. The total time, is called the term of the annuity. The regular periods, where the repayments are made, are called the payment periods.

Annuities, where the payments are made at the end of the payment period, are called ordinary annuities. When the payments are made at the beginning of the payment period, the process is called an annuity due.

The present value of the annuity involves 'moving' each of the payments R to the present. Not an easy task, for the monthly payments of a 25 year loan. Hence, the following mathematical formula can help: R per payment period, for n periods, at the rate r per period. For an illustration, if the plan is to get paid Rs. What will be the monthly repayments at 18 per cent compounded monthly?

Both loans require a repayment of equal monthly payments made at the end of the month for the next five years. What is the monthly payment? Assume 10 per cent compounded monthly Bring everything back to the present value.

It turns out that we can calculate this; using a loan amortisation formula. We can think of Arlene as lending the bank Rs. When a loan is repaid in equal instalments, part of the payment covers interest and the rest covers principal. The formula for paying back a loan in equal instalments is known as the amortisation formula. Plugging in Rs. This says that by lending investing her Rs. If there were no inflation, then Arlene would receive exactly Rs. If there is inflation of, say, 2 per cent per year, then the nominal interest rate will be 5 per cent and the real interest rate will be 3 per cent.

Arlene will receive Rs. That is, each year, her annuity payment will rise 2 per cent, in order to keep up with inflation. Adjusting for inflation is what makes this a real annuity. In the real world, there are some complications.

First, not all annuities are adjusted for inflation. Although inflation is important, all too often the elderly live on fixed incomes, which are annuities that do not adjust for inflation.

Second, insurance companies need to earn a profit. If the insurance company earns 0. This will www. If Arlene dies early, say in 5 years, she will not have collected her annuity and the insurance company earns a windfall gain. Conversely, if she defies the actuarial tables and lives for 25 years, the insurance company may take a loss, because the Rs. When interest-bearing debts are amortised by means of a series of equal payments at equal intervals, it is important to know how much goes for interest from each payment and how much goes for the reduction in principal.

For an illustration, this may be a necessary part of determining one's taxable income or tax deductions. We construct an amortisation schedule, which shows the progress of the amortisation of the debt.

Illustration A debt of Rs. Make out an amortisation schedule showing the distribution of the payments as to interest and the repayment of principal. Solution The interest due at the end of the first quarter is 2. The first payment of Rs. Thus, the outstanding principal after the first payment is reduced to Rs. The interest due at the end of the second quarter is 2. The second payment of Rs.

The outstanding principal now becomes Rs. This procedure is repeated and the results are tabulated below in the amortisation schedule.

It should be noted that the fifth payment is only Rs. The totals at the bottom of the schedule are for checking purposes. The total amount of principal repaid must equal the original debt. In addition, the total of the periodic payments must equal the total interest and the total principal returned. Note that the entries in the principal repaid column except the final payment are in the ratio.

This formula, can also be rewritten as. Investing this way to meet some future obligation is commonly called sinking fund. In problems 1 - 3 , you deposit Rs. How much will you have in the bank after 7 years? How much will you have in the bank after 25 years? How long will it take to have Rs. In problems 4 and 5, you deposit Rs.

How much will you have in the bank after one year? After four years? In problems 6 and 7, you deposit Rs. If you deposit Rs. Suppose that you deposit Rs. How much will you have after you make your deposit at the start of the tenth year?

Suppose that you want to have Rs. How much will you have to deposit each year? In the problems , suppose that you have Rs. What is the annuity payment? Suppose that the inflation rate is 2 per cent per year. What is the real interest rate that would be used to calculate a real annuity payment? Calculate the real annuity payment assuming that inflation is 2 per cent per year.

The annuity payment in the first year is equal to the real annuity payment. Calculate the annuity payment for the second year and for the third year. Suppose that you have Rs.

If the inflation rate is 5 per cent, calculate the real annuity. Calculate the actual annuity payments for each of the four years. Show that the annuity works. That is, for each year, fill out a table with the beginning balance, interest earned, annuity paid, and ending balance.

Show that after four years the ending balance is exactly zero. Do the same calculations as in the problem The formula for finding the monthly payment on a mortgage or an auto loan is the same as the formula for an annuity. However, the interest rate is the annual interest rate divided by 12, and the number of periods, n, is the number of years times Find the monthly payment on a thirty year mortgage with a Rs. Find the monthly payment on a five year auto loan with a Rs.

When a specified amount of money is needed at a specified future date, it is a good practice to accumulate systematically a fund by means of equal periodic deposits. Such a fund is called a sinking fund. Sinking funds are used to pay-off debts, to redeem bond issues, to replace worn-out equipment, to download new equipment, or in one of the depreciation methods. Since the amount needed in the sinking fund, the time the amount is needed and the interest rate that the fund earns are known, we have an annuity problem in which the size of the payment, the sinking-fund deposit, is to be determined.

A schedule www. Illustration 1. If you wish an annuity to grow to Rs. An annuity consists of monthly repayments of Rs. How much money will a student owe at graduation if she borrows Rs. A construction company plans to download a new earthmover for Rs. Determine the annual savings required to download the earthmover if the return on investment is 12 per cent.

A common method of paying off long-term loans is to pay the interest on the loan at the end of each interest period and create a sinking fund to accumulate the principal at the end of the term of the loan. Usually, the deposits into the sinking fund are made at the same times as the interest payments on the debt are made to the lender. The sum of the interest payment and the sinking-fund payment, is called the periodic expense or cost of the debt.

It should be noted that the sinking fund remains under the control of the borrower. At the end of the term of the loan, the borrower returns the whole principal as a lumpsum payment by transferring the accumulated value of the sinking fund to the lender. When the sinking-fund method is used, we detain the book value of the borrower's debt at any time as the original principal, minus the amount in the sinking fund.

The book value of the debt, may be considered as the outstanding balance of the loan. Illustration In 10 years, a Rs. A new machine at that time is expected to sell for Rs. In order to provide funds for the difference between the replacement cost and the salvage value, a sinking fund is set up into which equal payments are placed at the end of each year.

If the fund earns 7 per cent compounded annually, how much should each payment be? Simple Interest: When money is lent, the borrower usually pays a fee to the lender.

This fee is called 'interest' 'simple' interest or 'flat rate' interest. The amount of simple interest paid each year is a fixed percentage of the amount borrowed or lent at the start. Compound Interest: When interest is added to the account against returning it immediately to the customer, the interest itself earns interest during the next time period for computing interest. This is compounding of interest or more simply stated compound interest. Compounding Period: The time interval, between the moment at which interest is added to the account is called compounding period.

The rule allows us to determine the number of years it takes your money to double whether in debt or investment. Here is how to do it. Divide the number 72 by percentage rate you are paying on your debt or earning on your investment Annuities: They are essentially a series of fixed payments required from you or paid to you at a specified frequency over the course of a fixed period of time.

Sinking Fund: When there is a need for a specified amount of money at a specified future date, it is a good practice to accumulate systematically a fund by means of equal periodic deposits. Sinking funds are used to pay-off debts, to redeem bond issues, to replace worn- out equipment, to download new equipment, or in one of the depreciation methods.

Part A 1. A person invests Rs. A man saves every year Rs. Calculate the total amount of his savings at the end of the third year. The simple interest on a certain sum for 3 years is Rs. Find the rate of interest and the principal.

A sum of money is lent out at compound interest for two years at 20 per cent p. If the same sum of money is lent out at a compound interest at the same rate per cent per annum, C. Calculate the sum of money lent out. A man borrowed a certain sum of money and paid it back in 2 years in two equal instalments. If the rate of compound interest was 4 per cent per annum and if he paid back Rs. A sum of Rs. Find the annual payment. A loan of Rs.

The interest is compounded annually at 10 per cent. Find the value of each instalment. A man borrows Rs. He repays Rs. Calculate the amount outstanding at the end of the third payment. Give your answer to the nearest Re.

Find the amount which he has to pay at the end of the fourth year. Divide Rs. The rate of compound interest is 5 per cent per annum. Two partners A and B together invest Rs. After 3 years, A gets the same amount as B gets after 5 years. Find their shares in the sum of Rs. It looks at the current state of 'Big Audit' and the future of these firms. Dictionary of business and management This dictionary covers terminology used in ares of business and management including strategy, management, human resources, sales, marketing, insurance, finance and economics.

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It contains information on taxes, ISAs, pensions, investing across different assets and downloading property Financial regulation in the EU: from resilience to growth This publication looks to provide a bigger picture view of the impact and future of financial regulation in the EU, exploring the relationship between microeconomic incentives and macroeconomic growth, regulation and financial integration, and the changes required in economic policy to further European integration.

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Fundamentals of fund administration: a complete guide from fund set up to settlement and beyond Information about fund products and infrastructure for the benefit of managers.He should accept b The formula for calculating simple interest is as follows: When interest is added to the account against returning it immediately to the customer, the interest itself earns interest during the next time period for computing interest.

Thus, an annuity is a sequence of payments made at regular periods over a given time interval e. Calculate the NPV of the following project using a discount rate of 10 per cent: The company sets up a sinking fund to finance the replacement of the machine, assuming no change in price, with level payments at the end of each year. Company X is considering a piece of equipment that costs Rs. This is borne out by the fact that if the NPV figures, calculated by using discount rates of 10 per cent and 20 per cent, were used as the basis for interpolation, the results would be less accurate at At the end of the second year, two-fourths i.

However, the candidates could still refer to a few standard textbooks to supplement this www.