This key is labeled "interest per year" but it can handle any rate per different compounding
periods; for
example, ifwe have semiannual interest payments, our compounding
periods are semiannual and the
interest rate is the semiannual rate.
FV
Future value of the cash flows, this is a lump sum
PMT
Annuity (coupon) per discount period
PV
Present value of the cash flows, this is a lump sum
Calculator
inputs follow for the three examples
in Exhibit 7A.l. In these examples,
the unknown
value is the
price, which is the present value
(PV)
of the bond's
cash flows. (For additional
instruction
on entering
inputs i
a specific calculator,
or how to do more complicated
computations,
review the calculator's
user manual
or
revi
online calculator
tutorials.)
Example (1),Exhibit 7A.1: Bond pri.cedto,yield8%.
N
=
8 (4
years
x
2
periods per year =
8
semiannual periods)
l/Yr
=
4
(8% annual yield -;-2 periods per year =
4%
semiannually)
FV
=
100,000
(face value, which is the lump sum that must be repaid in the future)
PMT
=
4,000 ($100,000
x
4%
semiannual coupon rate)
I
PV
=
100,000
I
(output obtained from calculator)
Example (2),Exhibit 7A.1: Bond priced to yield 10%.
N=8
IlYr =
5
FV =
100,000
PMT =
4,000
I
PV =
93,537
Example (3),Exhibit 7A.1: Bond priced to yield 6%.
N=8
IlYr =
3
FV =
100,000
PMT =
4,000
I
PV =
107,020
Future Value Concepts
Future Value of a Single Amount
The
future value
of a single sum is the amount that a specific investment
is worth at a future date if invested
given rate of compound
interest.
To illustrate,
suppose
that we decide to invest $6,000 in a savings
account
pays
60/0
annual interest
and we intend to leave the principal
and interest
in the account for five years. We ass
that interest is credited
to the account
at the end of each year. The balance
in the account
at the end of five years
determined
using Table 3 in Appendix
A, which gives the future value of a dollar, as follows:
Principal
x Factor
=
Future Value
$6,000
x
1.33823
=
$8,029
The factor 1.33823 is at the intersection
of the row for five periods
and the column for 6%.
Next, suppose
that the interest
is credited
to the account
semiannually
rather than annually.
In this situati
there are 10 compounding
periods,
and we use a 3% semiannual
rate (one-half
the annual rate because
there
two compounding
periods per year). The future value calculation
follows:
Principal x Factor
=
Future Value
$6,000
x
1.34392
=
$8,064