Cost Accounting (14th Edition)

840 APPENDIX A NOTES ON COMPOUND INTEREST AND INTEREST TABLES
Fortunately, tables make key computations readily available. A facility in selecting the
proper table will minimize computations. Check the accuracy of the preceding answer
using Table 1, page 842.
Table 2—Present Value of $1
In the previous example, if $1,000 compounded at 8% per year will accumulate to
$1,259.70 in three years, then $1,000 must be the present value of $1,259.70 due at the
end of three years. The formula for the present value can be derived by reversing the
process of accumulation (finding the future amount) that we just finished.
If
then
S = P (1 + r ) n
P =
S
(1 + r ) n
In our example, S = $1,259.70, n = 3, r = 0.08, so
P = $1,259.70
(1.08) 3 = $1,000
Use Table 2, page 843, to check this calculation.
When accumulating, we advance or roll forward in time. The difference between our
original amount and our accumulated amount is called compound interest. When discounting,
we retreat or roll back in time. The difference between the future amount and
the present value is called compound discount. Note the following formulas:
Compound interest = P 3(1 + r ) n - 14
In our example, P = $1,000, n = 3, r = 0.08, so
Compound interest = $1,000 3(1.08) 3 - 14 = $259.70
Compound discount = Sc1 -
In our example, S = $1,259.70, n = 3, r = 0.08, so
Compound discount = $1,259.70c1 -
Table 3—Amount of Annuity of $1
1
(1 + r ) n d
1
(1.08) 3 d = $259.70
An (ordinary) annuity is a series of equal payments (receipts) to be paid (or received) at
the end of successive periods of equal length. Assume that $1,000 is invested at the end
of each of three years at 8%:
End of Year
0 1 2 3
Amount
1st payment $1,000.00 $1,080.00 $1,166.40, which is $1,000(1.08) 2
2nd payment $1,000.00 1,080.00, which is $1,000(1.08) 1
3rd payment
ƒ1,000.00
Accumulation (future amount) $3,246.40
The preceding arithmetic may be expressed algebraically as the amount of an ordinary
annuity of $1,000 for 3 years = $1,000(1 + r) 2 + $1,000(1 + r) 1 + $1,000.
We can develop the general formula for S n
, the amount of an ordinary annuity of $1,
by using the preceding example as a basis where n = 3 and r = 0.08:
1. S 3 = 1 + (1 + r ) 1 + (1 + r) 2