Amortization Charts
Compound Interest
C
ompound Interest or Compound Rate of Return (ROR) is the universal mathematical method used to measure the increase or decrease of all investments.
Example: We measure road distance by the mile, meat by the pound and Twinkies by the box. So we must master a method to measure the increase or decrease of all investments. In our illustrations, we will learn to measure return on examples of people making onetime lump sum investments and monthly periodic investments. You can also invest annually, quarterly, semi-annually plus other ways, but if we understand monthly and one-time investments we can easily understand the other methods. An example of a one-time investment would be depositing $1,000 in a savings account one time only. An example of monthly investing would be depositing $100 per month into a savings account over a period of time. We might want to know what each of these investments would be worth after a certain period of time. This can be done by using compound interest. You can do this by using compound interest tables or a financial calculator. Obviously, using a calculator would be faster, but since we all do not know how to use a financial calculator, we will use the compound interest tables. Compound interest tables are simply pre-calculated factors of what we want to figure out using investment amounts of $1. We simply plug our investment amount into the formula, find the factor on the chart and multiply. First, we will do an illustration using a one-time $1,000 investment to understand the process of compounding.
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COMPOUND INTEREST PROCESS FOR $1,000 LUMP SUM INVESTMENT
6%
Year 1 1000 x .06 60 1000 + 60 = 1060 1060 x .06 63.60 1060 + 63.60 = 1123.6 1123.6 x .06 67.42 1123.60 + 67.42 = 1191.02 1191.02 x .06 71.46 1191.02 + 71.46 = 1262.48 1262.48 x .06 75.75 1262.48 + 75.75 = 1338.23 1338.23 x .06 80.29 1338.23 + 80.29 = 1418.52 1418.52 x .06 85.11 1418.52 + 85.11 = 1503.63 Year 1
12
1000 x .12 120 1000 + 120 = 1120 1120 x .12 134.40 1120 + 134.40 = 1254.4 1254.4 x .12 150.53 1254.40 + 150.53 = 1404.93 1404.93 x .12 168.59 1404.93 + 168.59 = 1573.52 1573.52 x .12 188.82 1573.52 + 188.82 = 1762.34 1762.34 x .12 211.48 1762.34 + 211.48 = 1973.82 1973.82 x .12 236.86 1973.82 + 236.86 = 2210.68
Year 2
Year 2
Year 3
Year 3
Year 4
Year 4
Year 5
Year 5
Year 6
Year 6
Year 7
Year 7
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Rule of 72
T
here’s a quick formula which will get you close to the return of a one time investment only. This formula is only a rule of thumb, and works with a one time investment only. It is called the Rule of 72. You simply divide
72 by your rate of return and it will tell you how long it will take for your money to double.
72 / 2 = 36 – Your money will double every 36 years 72 / 6 = 12 – Your money will double every 12 years 72 / 12 = 6 – Your money will double every 6 years.
Rule of 72 Illustration Chart Years 4% 3 6 9 12 15 18 21 24 27 30 33 36 40,000 80,000 160,000 640,000 40,000 80,000 320,000 160,000 20,000 40,000 80,000 20,000 20,000 40,000 20,000 $10,000 One-Time Investment 6% 8% 12%
Tax consequences have not been considered.
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Compound Interest Discussion
Notice: Even though 12% rate of growth is twice as much as 6% rate of growth, the actual growth after compounding is much greater than twice, which is the SECRET
OF WEALTH.
One-Time Lump Sum Investment
We have looked at the process of compounding on money, let’s use the compound interest charts to obtain more details and get a quick practical way to measure the return on all investments. The first chart category is the Future Value of $1 with the interest added (compounded) monthly at a certain annual interest rate.
Example: You invest $1,000 one-time into an IRA and you want to know what it will be worth in 20 years at 8% annual rate compounded monthly. Simply turn to the Future Value chart, go to the 8% Annual Rate column, go down to 20 years and multiply the factor by $1,000. The answer is 1000 x 4.926803 = $4,926.80. Try a few on your own to get the swing of it. Illustration: Use a one-time lump sum $5,000 investment to fill in the chart below: Years Interest Rates
5.25% 10 20 30 8,443 14,256 24,071
9.5% 12,880 33,180
12% 16,502 54,463
85,474 179,748
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Lump Sum Investment to Reach A Specific Goal
We have looked at investing a lump sum and calculating what it will be worth at a specific time at a specific rate of return. Another twist to the lump sum investment is calculating how much money you must invest today to attain a specific dollar amount on a certain day.
Example: You want $200,000 in 20 years and you want to
know how much you must invest today at an 8% annual ROR to achieve your goal. The answer is simple to attain: Step 1–Turn to future value of dollar chart Step 2– Go to the 8% annual rate column Step 3– Go down to 20 years Step 4– Divide $200,000 by the factor $200,000 / 4.926803 = $40,594.28
Try a few on your own to get the swing of it. Illustration: Use a goal of $200,000 to fill in the Chart Below:
Lump Sum Needed to Attain $200,000
Years Interest Rates
5.25% 10 20 30 118,447 70,148 41,544
9.5% 77,638 30,138 13,577
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12% 60,599 18,361 5,563
Periodic Monthly Investment
We have reviewed compound interest for a one-time lump sum investment. Now let’s look at this process for monthly investments.
Example: You want to invest $100 a month into your IRA Account and you will earn 8% annual interest with the interest added (compounded) monthly. You plan to invest the $100 monthly for 20 years and want to know what your investment will be worth at the end of 20 years.
Simply turn to the Future Value Per Period Chart, go to the 8% annual rate column, go down to 20 years and multiply the factor by $100. The answer is $100 X 589.020416 = $58,902.04. Try a few to get the swing of it.
Illustration: Use $500 per month to fill in the chart below:
Periodic Monthly Investment Illustration Chart
Years 5.25% 10 20 30 78,688 211,555 435,905 Interest Rates 9.5% 99,540 355,961 1,016,517 12% 115,019 494,627 1,747,482
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Monthly Investment for Specific Goal At Specific Rate
We calculated what a specific monthly investment at a specific rate of return would be worth on a certain date. Let’s look at the opposite of this scenario.
Example: You want $500,000 in 20 years. You found an
investment that pays 8% annual rate of return. You need to know how much money you must invest monthly to obtain your goal. The answer is easy to calculate. Step–1 Turn to future value per period chart Step–2 Go to 8% annual rate of return column Step–3 Go down to 20 years Step–4 Divide $500,000 by the factor listed. ($500,000 / 589.020416 = $848.87) Try a few to get the swing of it.
Illustration: Use $500,000 as your goal to fill in the chart below:
Years 5.25% 10 20 30 3,177 1,182 574
Interest Rates 9.5% 2,512 702 246 12% 2,174 505 143
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Partial Payment to Amortize a $1
The next chart we will use is not really an investment chart, but it is very practical. Let’s see how to figure out monthly payments on monthly purchases before we buy them. This will help with cash flow management and projection. We can also use this chart to check on your current monthly payment schedules. Are you sure your car payment or house payment schedules were calculated correctly? Let’s do a few.
Example # 1: You are buying a new car for $33,000, you will pay $5,000 down payment and finance the remaining $28,000 for 5 years at 7% annual rate compounded monthly. What will your monthly payment be? The answer is easy to f i g u re out. Tu rn to the Partial Payment To Amortize Chart, go to the 7% annual rate column, go down to 5 years and multiply $28,000 by the factor. The answer is $28,000 x .019801 = $554.43 per month. Example # 2: You are buying a house for $140,000, you will pay $10,000 down payment and finance the remaining $130,000 at an annual interest rate of 6% compounded monthly. Your monthly payment for a 30 year mortgage will be how much? Turn to Partial Payment to Amortize $1 Chart, go to the 6% column, go down to thirty years and multiply $130,000 by the factor. The answer is $130,000 x .005996 = $779.48
To figure the payment for a 15 year mortgage, go through the same steps, but stop at the 15 year factor instead of the 30 year factor. The answer is $130,000 x .008439 = $1097.07 Practice and master all these compound interest charts, make good quantitative decisions and grow rich.
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