These lectures cover time value of money including discounting cash flow, interest compounding, present value of ordinary annuity, future value of annuity, future value of money.

Describe the fundamental concepts related to the time value of money. These techniques are being used in many areas of financial reporting where the relative values of cash inflows and outflows are measured and analyzed.

Compound interest, annuity, and present value techniques can be applied to many of the items found in financial statements. In accounting, these techniques can be used to measure the relative values of cash inflows and outflows, evaluate alternative investment opportunities, and determine periodic payments necessary to meet future obligations.

__Nature of Interest__

**Interest **is the payment for the use of money. It is normally stated as a percentage of the amount borrowed (principal), calculated on a yearly basis.

__Simple Interest__

**Simple**** interest is **computed on the amount of the principal only. The formula for simple interest can be expressed as *p* ×* i *×* n *where *p* is the principal,* i *is the rate of interest for one period, and* n* is the number of periods.

__Compound Interest__

**Compound interest **is the process of computing interest on the principal plus any interest previously earned. Compound interest is common in business situations where capital is financed over long periods of time. Simple interest is applied to short-term investments and debts due in one year or less. How often interest is compounded can make a substantial difference in the level of return achieved, or the cost of borrowing.

In discussing compound interest, the term **period **is used in place of **years **because interest may be compounded daily, weekly, monthly, and so on. To convert the **annual interest rate **to the **compounding period interest rate, **divide the annual interest rate by the number of compounding periods in a year. The number of periods over which interest will be compounded is calculated by multiplying the number of years involved by the number of compounding periods in a year.

The concept of **present value **is described as the amount that must be invested now to produce a known future value. This is the opposite of the compound interest discussion in which the present value was known and the future value was determined. An example of the type of question addressed by the present value method is: What amount must be invested today at 6% interest compounded annually to accumulate $5,000 at the end of 10 years? In this question the present value method is used to determine the initial dollar amount to be invested. The present value method can also be used to determine the **number of years **or the **interest rate **when the other facts are known.

An **annuity **is a series of equal periodic payments or receipts called **rents. **An annuity requires that the rents be paid or received at equal time intervals, and that compound interest be applied. The **future value of an annuity **is the sum (future value) of all the rents (payments or receipts) plus the accumulated compound interest on them. If the rents occur at the end of each time period, the annuity is known as an **ordinary annuity. **If rents occur at the beginning of each time period, it is an **annuity due. **Thus, in determining the amount of an annuity for a given set of facts, there will be one less interest period for an ordinary annuity than for an annuity due.

__Present Value of an Annuity__

The **present value of an annuity **is the present value of a series of equal rents, to withdraw at equal interests. If the annuity is an **ordinary annuity, **the initial sum of money is invested at the beginning of the first period and withdrawals are made at the end of each subsequent period. If the annuity is an **annuity due**, the initial sum of money is invested at the beginning of the first period and withdrawals are made at the beginning of each period. Thus, the first rent withdrawn in an annuity due occurs on the day after the initial sum of money is invested. When computing the present value of an annuity, for a given set of facts, there will be one less discount period for an annuity due than for an ordinary annuity.