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CH 8] Calculating Business 8-17

Computing Present Value at Compound Interest Present Value: It is
the current value of a
In economics and finance there are discussions on present value and future value. You future sum of money
have already been working with future value (FV) with compound interest on investments or stream of cash
and deposits of principal. The principal or principal investment has a value and that value is flows given a specified
rate of return.
its present value. Are you confused yet? Of course not.
Example The First National pays interest on savings accounts at 3¼% compounded daily.
If $3,000 is deposited, it will grow to how much in 6 weeks? (6 x 7 = 42 days) Time value of
money: (TVM) is the
Solution Note: For Exponents multiplied with hand calculator refer to page 8-11, 8-12, concept that money
& 8-13. available at the
present time is worth
n
S P = P( 1 + r/365) C I = S P — P more than the identical
S P = $3,000.00 ( 1 + (0.0325 / 365 )) 42 C I = $3,011.24—$3,000.00 sum in the future due
42
S P = $3,000.00 ( 1 + 0.00008904109) C I = $11.24 Growth in 6 weeks to its potential earning
42
S P = $3,000.00 ( 1.00008904109) capacity. This core
principle of finance
S P = $3,000.00 ( 1.00008904109) 7 x 2 x 3 holds that, provided
S P = $3,000.00 ( 1.0037465599) money can earn
interest, any amount of
S P = $3,011.24 money is worth more
In this example, “The First National pays interest on savings accounts at 3¼% compounded the sooner it is
daily. If $3,000 (present value) is deposited, it will grow to how much in 6 weeks?” The growth received. A dollar
or end value is that future value that is calculated with compound interest. today when put to work
and earning a return is
The present value will always be less than or equal to the future value because money
has interest earning potential and money put to work while you also work your job provides worth more than a
dollar tomorrow is
you with two sources of income and the creation of wealth. This interest earning potential of worth less in
money is a characteristic referred to as the time value of money. Time value can be purchasing power as
described with the simplified phrase, "A dollar today is worth more (purchases more) rising costs and
than a dollar tomorrow unless that dollar is working". A dollar working for you defeats inflation devalue your
inflation. money. A dollar
working for you
Interest paid is the cost of money. When you borrow money, the interest you pay for its defeats inflation.
use is the cost to you to use that money. When you deposit your money in a savings
account or an investment, the interest you receive is the cost of the use of your money. Future value: (FV)
Interest is the cost of money for the borrower or the investor. By letting the borrower have is the value of a
access to the money, the lender has sacrificed the exchange value of this money, and is current asset at a
compensated for it in the form of interest. The initial amount of the borrowed funds, the specified date in the
present value (PV), is less than the total amount of money paid for its use, the future value future based on a
(FV). defined rate of. growth
For time value, the present value of a compounded amount that is due in the future is
the principal and when invested now at a given interest rate per period, will grow to the
compounded amount, reaching a greater value, defeating inflation while maintaining or Purchasing Power:
increasing purchasing power. As purchasing power is the ability to purchase goods and Purchasing power is the
services, it is reasonable to understand $3,000 today will not purchase as much as $4,000 value of a currency
can purchase today. Over time $4,000 will purchase less because inflation causes prices to expressed in terms of
the amount of goods or
rise. Therefore, purchasing power becomes important, all else being equal, because services that one unit of
inflation decreases the amount of goods or services you would be able to purchase. This is money can buy.
the effect inflation has on the prices for goods and services: it takes more dollars to
purchase those same goods and services. If your money does not increase then you will only
be able to purchase fewer goods and services than before. It is easy to understand that your
money needs to work for you and increase if only to keep ahead of inflation.
Having a good understanding of present value and future value of money is essential for 8
money management.
Consider: Money invested at 6% interest compounded semiannually, the value of $1 Inflation: In business
grows to $1.0609 in one year. 6% annual becomes (6% ÷ 2 =) 3% semiannually. The and economics it is a
arithmetic is: general increase in
prices and fall in the
n
2
2
($1 + 0.03) = ($1 + 0.03) = $1.03 = ($1.03 x $1.03 =) $1.0609, thus $1.0609 > $1.00 purchasing value of
money.
From the perspective of the future value we could say that the present value of
$1.0609 is $1. It is obvious that as money has earning power, its future value needs to be
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