12-1 Compound Interest. 12-2 Compound Interest and Present Value.

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12-1 Compound Interest

Transcript of 12-1 Compound Interest. 12-2 Compound Interest and Present Value.

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Compound Interest

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Compound Interest and Compound Interest and Present ValuePresent Value

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• 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

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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

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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

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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

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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

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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

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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.

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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

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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

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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.

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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