12-1 compound interest. 12-2 compound interest and present value
TRANSCRIPT
12-1
Compound Interest
12-2
Compound Interest and Compound Interest and Present ValuePresent Value
12-3
• Compare simple interest with compound interest
• Calculate the compound amount and interest manually.
• Explain and compute the effective rate
Compound Interest and Present Value
Learning Unit ObjectivesCompound Interest (Future Value) – The Big Picture
12-4
Compounding Interest (Future Value)
Compound interest - the interest on the principal plus the interest
of prior periods
Compounding - involves the calculation of interest
periodically over the life of the loan or investment
Present value - the value of a loan or investment today
Future value (compound amount) - is the final amount of the loan or investment at the end of the last
period
12-5
Future Value of $1 at 8% for Four Periods
$0.00$0.50$1.00$1.50
$2.00$2.50$3.00$3.50$4.00$4.50$5.00
0 1 2 3 4
Number of periods
Compounding goes from present value to future value
Present value
After 1 period $1 is
worth $1.08
After 2 periods
$1 is worth $1.17
After 3 periods
$1 is worth $1.26
Future Value
After 4 periods
$1 is worth $1.36
$1.00 $1.08 $1.1664
$1.2597
$1.3605
12-6
Compounding Terms
Compounding Periods Interested Calculated
Compounding Annually Once a year
Compounding Semiannually Every 6 months
Compounding Quarterly Every 3 months
Compounding Monthly Every month
Compounding Daily Every day
Compounding fortnightly Every two weeks
12-7
Tools for Calculating Compound Interest
Number of periods (N) Number of years
multiplied the number of times the interest is compounded per year
Rate for each period (R) Annual interest rate divided by the number of times the interest is compounded per year
If you compounded $100 for 3 years at 6% annually, semiannually, or quarterly What is N and R?
Annually: 3 x 1 = 3Semiannually: 3 x 2 = 6Quarterly: 3 x 4 = 12
Annually: 6% / 1 = 6%Semiannually: 6% / 2 = 3%Quarterly: 6% / 4 = 1.5%
Periods Rate
12-8
Simple Versus Compound Interest
Al Jones deposited $1,000 in a savings account for 5 years at
an annual interest rate of 10%. What is Al’s simple interest
and maturity value?
I = P x R x T
I = $1,000 x .10 x 5
I = $500
Amount of money = $1,000 + $500
= $1,500
I = P x R x T
I = $1,000 x .10 x 5
I = $500
Amount of money = $1,000 + $500
= $1,500
Al Jones deposited $1,000 in a savings account for 5 years at an annual compounded rate of 10%. What is Al’s interest
and compounded amount?
Simple CompoundedCompoundedCompoundedCompounded
Year 1 Year 2 Year 3 Year 4 Year 51,000.00$ 1,100.00$ 1,210.00$ 1,331.00$ 1,464.10$
x .10 x .10 x .10 x .10 x .10Interest 100.00$ 110.00$ 121.00$ 133.10$ 146.41$ Beg. Bal 1000.00 1100.00 1210.00 1331.00 1464.10End of year 1,100.00$ 1,210.00$ 1,331.00$ 1,464.10$ 1,610.51$
Interest: $1,610.51 - $1,000 = $610.51
12-9
Calculating Compound Amount by Table Lookup
Step 1. Find the periods: Years multiplied by number of times interest is compounded in 1 year
Step 2. Find the rate: Annual rate divided by number of times interest is compounded in 1 year
Step 3. Go down the period column of the table to the number desired; look across the row to find the rate. At the intersection is the table factor
Step 4. Multiply the table factor by the amount of the loan.
12-10
Period 1% 1.50% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 1.0100 1.0150 1.0200 1.0300 1.0400 1.0500 1.0600 1.0700 1.0800 1.0900 1.1000
2 1.0201 1.0302 1.0404 1.0609 1.0816 1.1025 1.1236 1.1449 1.1664 1.1881 1.2100
3 1.0300 1.0457 1.0612 1.0927 1.1249 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310
4 1.0406 1.0614 1.0824 1.1255 1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641
5 1.0510 1.0773 1.1041 1.1593 1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105
6 1.0615 1.0934 1.1262 1.1941 1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716
7 1.0721 1.1098 1.1487 1.2299 1.3159 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487
8 1.0829 1.1265 1.1717 1.2668 1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436
9 1.0937 1.1434 1.1951 1.3048 1.4233 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579
10 1.1046 1.1605 1.2190 1.3439 1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937
11 1.1157 1.1780 1.2434 1.3842 1.5395 1.7103 1.8983 2.1049 2.3316 2.5804 2.8531
12 1.1260 1.1960 1.2682 1.4258 1.6010 1.7959 2.0122 2.2522 2.5182 2.8127 3.1384
13 1.1381 1.2135 1.2936 1.4685 1.6651 1.8856 2.1329 2.4098 2.7196 3.0658 3.4523
14 1.1495 1.2318 1.3195 1.5126 1.7317 1.9799 2.2609 2.5785 2.9372 3.3417 3.7975
15 1.1610 1.2502 1.3459 1.5580 1.8009 2.0789 2.3966 2.7590 3.1722 3.6425 4.1772
Future value of $1 at compound interest (Partial)
- Future Value of $1 at Compound Interest
12-11
Calculating Compound Amount by Table Lookup
Steve Smith deposited $6,000 in a savings account for 5 years at an semiannual compounded rate of 10%. What is Steve’s interest and compounded amount?
N = 5 x 2 = 10
R = 10% = 5% 2
Table Factor = 1.6289
Compounded Amount:
$6,000 x 1.6289 = $9,773.40
I = $9,773.40 - $6,000 = $3,773.400
200
400
600
800
1000
1200
1400
2002 2003 2004 2005
Investment
12-12
Nominal and Effective Rates of Interest
Truth in
Savings
Law
Annual
Percentage
YieldFlat Rate = Interest for 1 year
Principal
Nominal Rate (Stated Rate) - The rate on which the bank calculates interest.
12-13
Compounding Interest Daily
Calculate what $2,000 compounded daily for 7 years will grow to at 6%pa
T = 7 years
R = 6%
A=P(1+r)n
=$2,000 ( 1+ 0.06)7= $3,007.3