Single Payment Compound Interest Formulas 75If $500 were deposited in a bank savings account, how much would be in the account three years
hence if the bank paid 6% interest [email protected]~Jy?
We can draw a diagram of the problem.[Note:To have a consistent notation, we will repre-
sentreceiptsby upward arrows (and positive signs), anddisbursements(or payments) will have
downward arrows (and negative signs).].SQlUl1I0N
From the viewpoint of the person depositingthe $500, the diagram for "today" (Time=0) through
Year 3 is as follows:Receipts (+$)F=?r
Disbursements (-$)0-1-2-3t n=3
P= 500 i= 0.06We need to identify the various elements of the equation. The present sumPis $500. The interest
rate per interest period is 6%, and in 3 years there are three interest periods. The future sumFis
to be computed from the formula
F=P(1+it =500(1 + 0.06)3=$595.50
whereP= $500,i= 0.06,n=3, andFis unknown.
Thus if we deposit $500 in the bank now at 6% interest, there will be $595.50 in the account
in three years.
The equationF=P(I +i)nneed not be solved with a hand calculator.Instead,the singlepayment
compound amount factor,(1 +i)n,is readily determined from computed~tables~The factor is
written in convenient notation as
=(1 +i)n= (F j P, i, n)
= ;;:= =
and in functional notation as
(Fj P,6%, 3) r
,Knowingn = 3, locate the proper row in the 6% table.2 To findFgivenP,look in the ~st
column, which is headed "Single Payment, Compound 1.mountFactor": forn =3,we find 1.191.
IN ~_ -- - ...--
2The appendix contains compound interest tables for rates between 1/4 and 60%.