Unformatted text preview: 1 0 ower Point Presentation designed by Dr. Sylvia C. Hudgins for Finance 323 at ODU Compound Value
Parameters:
Interest rate (i) [The text uses r in notation]
Interest
Amount that is invested, present value (PV)
Time money remains invested (n)
Future value of the investment in n years (FVn)
Periodic equal payment (or deposit) (PMT) 2 Compound Value 3 Future Value of a Lump Sum (one time payment): Value at some time in the future of an investment Interest compounds: earn interest on interest in later
Interest
years.
years. Future value in one year is present value plus the
Future
interest that is earned over the year.
interest Compound Value 4 Future Value of a Lump Sum (one time payment): Value at some time in the future of an investment Interest compounds: earn interest on interest in later
Interest
years.
years. Future value in one year is present value plus the
Future
interest that is earned over the year.
interest FV1 = PV + (PV x i)
Example: Invest $100 for 1 year at 6%: FV1 = 100 + (100 x 0.06) = $106.00 5 Compound Value Future Value of a Lump Sum (one time payment): Extend to 2 years:
FV2 = PV + (PV x i) + (PV x i) + PV x i x i 1st year
interest on
Principal 2nd year
interest on
Principal 2nd year
interest on
interest FV2 = 100 + (100 x.06) + (100 x .06) + (100 x .06 x .06) = 112.36 In General: FVn = PV(1+ i)n Compound Value 6 Future Value of a Sum (one time payment): Example: Deposit $256 at an 8% interest rate, how
Example:
much can you withdraw in 1 year, 2 years, 16 years?
much
FV1 = 256+256(0.08) = $276.48
FV2 = 256+256(0.08)+256(0.08)+256(.08).08
= 256+20.48+20.48+1.64 = $298.60
= 256(1+.08)2 = $298.60
FV16 = 256(1+.08)16 = $877.08 7 Compound Value
Future Value of a Sum (one time payment): Graphically: Deposit $256 today, what is Future
Graphically:
Value?
Value?
$1000
900 i = 8% 800
700
600
500 i = 4% 400
300
200
0 i = 0% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Year Compound vs. Simple Interest 8 Compound interest: Interest earned on both the
Compound
initial principal and the interest reinvested from
prior periods.
prior
Simple interest : Interest earned only on the
Simple
original principal amount invested.
original
Consider the previous example(Deposit $256 at
Consider
an 8% interest rate, how much can you withdraw
in 16 years?
in
FV with compound interest = 877.08
FV with simple interest = 256 + (16*20.48) =
583.68
The extra 293.40 comes from the interest paid on
the interest 9 Discounted Value Present Value of a Lump Sum (one time payment): Value today of an amount to be received or paid in
Value
the future.
the FV n
PV =
(1 + i)n
Example: Expect to receive $100 in one year. If can invest
at 10%, what is it worth today?
0 PV = 100 = 90.90 (1+.1) 1 $100 2 10 Discounted Value Present Value of a Lump Sum (one time payment): Value today of an amount to be received or paid in
Value
the future.
the FV8
PV =
(1 + i)8
Example: Expect to receive $100 in EIGHT years. If can
invest at 10%, what is it worth today?
0 100 = 46.65
PV =
(1+.1)8 1 2 3 4 5 6 7 8 $100 11 Discounted Value Present Value of a Sum (one time payment): Graphically: Present Value of $100 to be received in
Graphically:
the future.
the
$100
90 i = 0% 80
70
60 i = 5% 50
40
30
20
0 i = 10% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Year Financial Calculator
Setting Display Should show 9 decimal places on your
Should
calculator when you are performing
calculations.
calculations. Financial calculators contain a number of
Financial
memory registers. These registers should be
cleared of work to prevent carryover errors.
(CLR TVM)
(CLR Compounding should be set to once per
Compounding
period (P/YR=1), not the factory setting of
12.
12. 12 13 Compound Value Future Value of a Sum (one time payment): Example: Deposit $256 at an 8% interest rate, how
Example:
much can you withdraw in 16 years?
much
FV16 = 256(1+.08)16 = $877.08
Interest rate (i)=
Amount that is invested (PV)=
(Remember sign convention) number of periods (n)=
Future value (FVn)=
Periodic equal payments
Periodic
(PMT)=0
(PMT)=0 877.08 N 16 I/YR PV PMT FV 8 256 0 ? 14 Discounted Value Present Value of a Lump Sum (one time payment):
Example: Expect to receive $100 in EIGHT years. If can
invest at 10%, what is it worth today? 100 = 46.65
PV =
(1+.1)8
Interest rate (i)=
Amount that is invested (PV)=
number of periods (n)=
Future value (FVn)=
Periodic equal payments
Periodic
(PMT)=0
(PMT)=0 46.65 N 8 I/YR PV PMT FV 10 ? 0 100 15 Compound/Discounted Value Solve for other parameters (I/YR) Given any three of the following: PV, FV, i and n, the
Given
fourth can be computed.
fourth
Example: A $200 investment has grown to $230 over two
years. What is the ANNUAL return on this
investment?
0
1
2
$200 $230 Can Solve Using Either: FVn
PV =
or FVn = PV(1+ i)n
(1 + i)n
In General:
In i= ( FV
PV 1
n ) 1 230 = 200(1+ i)2
230
= (1+ i)2
200
1.15 = (1+ i)2
1.0724 = 1+ i
i = .0724 = 7.24% 16 Compound/Discounted Value Solve for other parameters (N) Given any three of the following: PV, FV, i and n, the
Given
fourth can be computed.
fourth
Example: How long will it take for a $300 investment to
grow to $500 if 6% annual interest is earned?
0 $300 1 N $500
Can Solve Using Either:
500 = 300(1+ .06)N
FVn
PV =
or FVn = PV(1+ i)n 500 = (1+ .06)N
(1 + i)n
300
ln(1.667) = N ln(1+ .06)
General Formula:
N = ln(1.667)
ln (FV/PV)
ln(1.06)
N = ln (1 + i)
N = 8.77 years Quick Quiz: 17 What is the difference between simple interest and
What
compound interest? (How would you calculate
each?)
What is the relationship between present value
and future value? (How would you calculate
each?)
What are some situations where you might want to
compute the implied interest rate? (How would
you calculate the interest rate?) (Remember the
sign convention on the calculator)
sign
When might you want to compute the number of
When
periods? (How would you calculate the number
of periods?)
of ...
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Full Document
 Spring '08
 Staff
 Managerial Accounting, Time Value Of Money, Mathematical finance

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