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If you need some instruction in Excel—or a refresher—get started now. You will find links for
Excel tutorials at the end of this chapter.
To see explanations and illustrations of using Excel for financial calculations involving the time
value of money, check out the Web site for this chapter.
Further and more advanced uses of the time value of money will be found in Chapter 6, “Planning
Capital Expenditure.” To understand what we mean by time value of money, we will look at various
measures used to determine the value of money over time.
Future Value
The future value of a dollar amount put into a savings account reflects what we expect the value of
that dollar amount to be in a fixed amount of time, or how we expect the money to grow. Growth or,
in the case of a savings account, the interest rate paid, is the amount that we expect to receive above
the amount that we have deposited.
For example, on Billy‟s 10th birthday his aunt opens a savings account in his name and deposits
$50 into that account. Over the years, Billy forgets that he has this bank account, and at the age of 20,
he finds the passbook stuffed in the back of a drawer. When he opens the passbook, he remembers the
birthday gift of $50 from his aunt. For Billy, this $50 is just the amount he needs to purchase a new
pair of jeans.
Exhibit 4.1 How Billy’s savings account grew.
Billy goes to the bank, presents the passbook, and requests to withdraw $50, assuming this will zero
out his balance and close the account. After a few moments, the teller hands Billy the $50 he requested
and returns his passbook. Before leaving the bank, Billy looks in his passbook and sees that he still has
a balance of $31.44. It dawns on him that his account has earned interest on the initial amount of the
savings. Let us analyze why Billy still has money in that account and how the $50 grew to a balance
of $81.44. For this example, we will assume that the annual rate of interest that the bank paid over the
10 years remained fixed at 5%.
The initial balance was $50 with an annual interest rate of 5%. This means that at the end of the first
year the balance was $50 + ($50 × 5%) or $50 + $2.50, which totals $52.50. The $2.50 is the amount
earned from interest. Interest in this account is compound interest, which means that interest is earned