BASIC CONCEPTS
Time Value of Money
The key to solving the problem described in the financial reporting case is an understanding of the concept commonly referred to as the time value of money . This concept means that money invested today will grow to a larger dollar amount in the future. For example, $100 invested in a savings account at your local bank yielding 6% annually will grow to $106 in one year. The difference between the $100 invested now—the present value of the investment—and its $106 future value represents the time value of money.
This concept has nothing to do with the worth or buying power of those dollars. Prices in our economy can change. If the inflation rate were higher than 6%, then the $106 you would have in the savings account actually would be worth less than the $100 you had a year earlier. The time value of money concept concerns only the growth in the dollar amounts of money. The concepts are useful in solving business decisions such as the determination of the lottery award presented in the financial reporting case. More important, the concepts are necessary when valuing assets and liabilities for financial reporting purposes. Most accounting applications that incorporate the time value of money involve the concept of present value. The valuation of leases, bonds, pension obligations, and certain notes receivable and payable are a few prominent examples. It is important that you master the concepts and tools we review here as it is essential for the remainder of your accounting education.
Simple versus Compound Interest
Interest is the “rent” paid for the use of money for some period of time. In dollar terms, it is the amount of money paid or received in excess of the amount of money borrowed or lent. If you lent the bank $100 today and “received” $106 a year from now, your interest earned would be $6. Interest also can be expressed as a rate at which money will grow. In this case, that rate is 6%. It is this interest that gives money its time value.
Simple interest is computed by multiplying an initial investment times both the applicable interest rate and the period of time for which the money is used. For example, simple interest earned each year on a $1,000 investment paying 10% is $100 ($1,000 × 10%). Compound interest results in increasingly larger interest amounts for each period of the investment. The reason is that interest is now being earned not only on the initial investment amount but also on the accumulated interest earned in previous periods. For example, Cindy Johnson invested $1,000 in a savings account paying 10% interest compounded annually. How much interest will she earn each year, and what will be her investment balance after three years?
Time Value of Money
The key to solving the problem described in the financial reporting case is an understanding of the concept commonly referred to as the time value of money . This concept means that money invested today will grow to a larger dollar amount in the future. For example, $100 invested in a savings account at your local bank yielding 6% annually will grow to $106 in one year. The difference between the $100 invested now—the present value of the investment—and its $106 future value represents the time value of money.
This concept has nothing to do with the worth or buying power of those dollars. Prices in our economy can change. If the inflation rate were higher than 6%, then the $106 you would have in the savings account actually would be worth less than the $100 you had a year earlier. The time value of money concept concerns only the growth in the dollar amounts of money. The concepts are useful in solving business decisions such as the determination of the lottery award presented in the financial reporting case. More important, the concepts are necessary when valuing assets and liabilities for financial reporting purposes. Most accounting applications that incorporate the time value of money involve the concept of present value. The valuation of leases, bonds, pension obligations, and certain notes receivable and payable are a few prominent examples. It is important that you master the concepts and tools we review here as it is essential for the remainder of your accounting education.
Simple versus Compound Interest
Interest is the “rent” paid for the use of money for some period of time. In dollar terms, it is the amount of money paid or received in excess of the amount of money borrowed or lent. If you lent the bank $100 today and “received” $106 a year from now, your interest earned would be $6. Interest also can be expressed as a rate at which money will grow. In this case, that rate is 6%. It is this interest that gives money its time value.
Simple interest is computed by multiplying an initial investment times both the applicable interest rate and the period of time for which the money is used. For example, simple interest earned each year on a $1,000 investment paying 10% is $100 ($1,000 × 10%). Compound interest results in increasingly larger interest amounts for each period of the investment. The reason is that interest is now being earned not only on the initial investment amount but also on the accumulated interest earned in previous periods. For example, Cindy Johnson invested $1,000 in a savings account paying 10% interest compounded annually. How much interest will she earn each year, and what will be her investment balance after three years?
With compound interest at 10% annually, the $1,000 investment would grow to $1,331 at the end of the three-year period. If Cindy withdrew the interest earned each year, she would earn only $100 in interest each year (the amount of simple interest). If the investment period had been 20 years, 20 calculations would be needed. However, calculators, computer programs, and compound interest tables make these calculations easier
Most banks compound interest more frequently than once a year. Daily compounding is common for savings accounts. More rapid compounding has the effect of increasing the actual rate, which is called the effective rate , at which money grows per year. It is important to note that interest is typically stated as an annual rate regardless of the length of the compounding period involved. In situations when the compounding period is less than a year the interest rate per compounding period is determined by dividing the annual rate by the number of periods. Assuming an annual rate of 12%:
Most banks compound interest more frequently than once a year. Daily compounding is common for savings accounts. More rapid compounding has the effect of increasing the actual rate, which is called the effective rate , at which money grows per year. It is important to note that interest is typically stated as an annual rate regardless of the length of the compounding period involved. In situations when the compounding period is less than a year the interest rate per compounding period is determined by dividing the annual rate by the number of periods. Assuming an annual rate of 12%:
As an example, now let’s assume Cindy Johnson invested $1,000 in a savings account paying 10% interest compounded twice a year. There are two six-month periods paying interest at 5% (the annual rate divided by two periods). How much interest will she earn the first year, and what will be her investment balance at the end of the year
The $1,000 would grow by $102.50, the interest earned, to $1,102.50 , $2.50 more than if interest were compounded only once a year. The effective annual interest rate, often referred to as the annual yield, is 10.25% ($102.50 ÷ $1,000).
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