Unformatted text preview: 1 0 ower Point Presentation designed by Dr. Sylvia C. Hudgins for Finance 323 at ODU 2 NonAnnual Compounding All equations and calculator solutions thus far have
All
assumed compounding occurs ONCE a year.
assumed
Example: Deposit $1,000 at 10% nominal annual interest rate.
How much will you have at end of 1 year?
ANNUAL COMPOUNDING
0 $1,000 1 $1,000(1.1) $1,100 SEMIANNUAL COMPOUNDING
0 $1,000 6 months $1,000(1.05) 1 Earn 10%/2=5%
each compounding
period $1,050 $1,050(1.05) $1,102.50 3 NonAnnual Compounding All equations and calculator solutions thus far have
All
assumed compounding occurs ONCE a year.
assumed When compounding more than once a year, must
When
adjust formula FV n = i mn
PV(1+ m) m = # of compounding
periods in a year Example: Deposit $1,800 at 8% nominal annual interest rate,
compounded quarterly. How much will you have at
end of 3 years?
.08 4•3
FV3 = 1,800(1+ 4 )
12 = 1,800(1.02)
= 1,800(1.2682) = 2,282.84 4 NonAnnual Compounding When compounding more than once a year, the term
When
Effective Annual Rate (EAR) is useful for comparisons.
Effective Effective Annual Rate (EAR) is the interest rate
Effective
expressed as if it were compounded once per year.
expressed EAR = im
(1+m) m = # of compounding
periods in a year 1 Example: Deposit $1,800 at 8% nominal annual interest rate,
compounded quarterly. What is the EAR?
.08 4
(1+ 4 )  EAR =
= .08243
= 8.24% 1 NonAnnual Compounding Compounding
period
period
Year
Year
Quarter
Quarter
Month
Month
Week
Week
Day
Day
Hour
Hour
Minute
Minute Number of times Effective
compounded
annual rate
1
10.00000%
4
10.38129
12
10.47131
52
10.50648
365
10.51558
8,760
10.51703
525,600
10.51709 5 6 Future Value of an Annuity Annuity string of deposits with constant value and
Annuityfixed interval.
fixed
0 1 2 $0 $100 3 $100 $100
$100(1.08)
$108
$100(1.08)2
$116.64
Compute FV3
$324.64
How much would this account have in it at the end of 3
years if interest were earned at a rate of 8% annually? FVAN = N (1+i)  1
PMT( i ) 3 = 100( (1+.08)  1 )
....
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Full Document
 Spring '08
 Staff
 Managerial Accounting, Interest Rates, Time Value Of Money, PV PMT FV, I/YR PV PMT

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