FCS 3450
Fall 2015
Unit 3
Microeconomics and
Macroeconomics
Concept 8: Future Value (FV)
What is future value?
• Accumulated amount of your investment fund.
P = principle (original invested amount)
r = interest rate for a certain period
n = number of periods
In this calculation, all periods have to be the same.
Simple Interest vs. Compounding
Interest
Simple interest means you receive interest on original amount invested only.
Compound interest means you receive interest on both the original amount invested and the
interest rate you made from the investment (interest on interest).
Effect of Compound Interest
Simple Interest
Year Principal
1
100.00
2
100.00
3
100.00
4
100.00
5
100.00
6
100.00
7
100.00
8
100.00
9
100.00
10
100.00
11
100.00
12
100.00
13
100.00
14
100.00
15
100.00
16
100.00
17
100.00
18
100.00
Rate Time
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
Interest
Earned
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
10.00
180.00
Compound Interest
New
Balance
110.00
120.00
130.00
140.00
150.00
160.00
170.00
180.00
190.00
200.00
210.00
220.00
230.00
240.00
250.00
260.00
270.00
280.00
Principal
100.00
110.00
121.00
133.10
146.41
161.05
177.16
194.87
214.36
235.79
259.37
285.31
313.84
345.23
379.75
417.72
459.50
505.45
Rate
Time
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
10%
1
Interest
Earned
10.00
11.00
12.10
13.31
14.64
16.11
17.72
19.49
21.44
23.58
25.94
28.53
31.38
34.52
37.97
41.77
45.95
50.54
455.99
New
Balance
110.00
121.00
133.10
146.41
161.05
177.16
194.87
214.36
235.79
259.37
285.31
313.84
345.23
379.75
417.72
459.50
505.45
555.99
TM 1-7
THE IMPACT OF TIME VALUE OF MONEY AT 9% INTEREST
Contributions
Contributions
Age
Made Early
Age
Made Later
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
$ 2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
$
0
0
0
0
0
0
0
0
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
2,000
Amount available
at age 65:
$579,471
Total
of
$18,000
Invested
0
$470,249
Total
of
$70,000
Invested
The Difference Between Simple Interest and
Compound Interest
• Simple Interest is the interest computed on principal only
Interest
= Principle x Rate x Time or I = P x R x T.
• Compound Interest is the calculation of interest on interest as well as interest on the
original investment.
Future Value of $10,000 with Interest Compounded Annually
$600,000
$500,000
14%
$400,000
12%
$300,000
10%
8%
$200,000
6%
$100,000
$0
0
10
20
30
Future Value for One-Time Investment
To compute future value for one-time investment, one used Future Value
Factor (FVF).
What is the Future Value Factor (FVF)?
𝑛
• FVF = (1 + r)
What does FVF mean?
FVF is how much one dollar will generate in the future given interest rate r
and n periods.
How do you use FVF to figure out the future value of one-time
investments?
𝑛
FV = P*FVF = P*(1 + r)
Rule of 72
• A handy formula to calculate the number of years it
takes to double principal using compound interest is the
Rule of 72. You simply divide the interest rate the
money will earn into the number 72. For example, if
interest is compounded at a rate of 7 % per year, your
principle will double every 10.3 years. If the rate is 6 %,
it will take 12 years.The rule of 72 also works for
determining how long it would take for the price of
something to double given a rate of increase in the
price. For example, if college tuition costs are rising 8 %
per year, the cost of college education doubles in just
over nine years.
The Rule of 72
18
16
14
12
10
8
6
4
2
0
12% 10% 8% 6% 4%
Future Value Example
You put $10,000 in a CD account for 2
years. The account pays 4% annual interest.
How much money will you have at the end
if annual compounding interest is used?
How about monthly compounding? How
about daily compounding?
Future Value Calculations
Annual compounding:
FV = $10,000 * (1+4%)^2 = $10,000 x 1.08160 = $10,816.00
Monthly compounding: (monthly interest rate = 4%/12 = 0.3333 %; n=2*12 = 24
FV = $10,000 * (1+0.3333%) ^24 = $10,000 x 1.083134 = $10,831.34
Daily compounding: (daily interest rate – 4%/365 = 0.0110%, n = 2*365 = 730
FV = $10,000 * (1+.0110%)^730 = $10,000 * 1.083607 = $10,836.07
FV of Periodical Investments (Annuity)
Periodical investments, or annuities, are multiple investments
that are made at certain time intervals (every day, month,
year, etc.)
Example of Periodic Investment
Suppose you have decided to save some money for a
vacation. You can afford to save $100 month. You believe you
can earn 8% on your money, compounded monthly. How
much money will you have at the end of the 12th month?
Applying FVA calculation
Beginning of the month formula:
FVFS = 1 + 𝑟
𝑛
+ 1+𝑟
𝑛−1
1
1+𝑟
+. . . . . + 1 + 𝑟
=
𝑟 𝑛+1 −1
𝑟
−1
0
𝑟 𝑛 −1
𝑟
−1
End of the month formula:
FVFS = 1 + 𝑟
𝑛−1
+ 1+𝑟
𝑛−2 +. . . . . +
=
FVA Calculation
FVA = Pp * FVFS
Where Pp = amount of periodic payments
Future Value Factor of an Annuity (FVA)
Beginning of the month formula:
FVA = Pp x FVFS (r= 8%/12 = 0.6667%, n = 12, BOM)
(1+𝑟 𝑛+1 −1
FVA Pp *
−1
𝑟
1+0.6667% 12+1 −1
=$100 *
−
0.6667%
1
=$100 * 12.5330 = $1,253.30
Future Value of a Dollar (Single Payment)
Future Value of a Series of Annual Deposits (Annuity)
Present Value of a Dollar (Single Payment)
Present Value of a Series of Annual Deposits (Annuity)
Keeping the Time Value of Money Formulas Straight
Do I have the money now?
Yes
Yes
No
Use Future
Value Table
Use Present Value
Table
Is it a lump sum?
Is it a lump
sum?
No
Yes
Use PV
Use FV
Use FVA
No
Use PVA
The Time Value of Money in Decision Making
• Assume you have the option of two different investment options. First, a friend wanted
to borrow $5,000 for three years and pay you back $6,000 in a lump sum. Second, you
could invest the same $5,000 for three years in a government bond paying 7 percent
annual interest. Which investment would be the best financial decision?
FV = (PV)(1 + r) n
= (5,000)(1+.07)3
= 5,000 x 1.225043
= $6,125.22
You would earn $125.22 more by investing in the government bonds.