Baldwin’s PreCalculus Collection

of

Financial Growth Concepts

r = annual interest rate        k = number of periods per year         t = number of years             P = principal         

Compound Interest                                           

Ex: $1200 into a savings account for 3 years at 3% compounded monthly =

 

Continuously Compounded                            

Ex:  $1200 into a savings account for 3 years at 3% compounded continuously =

Effective Yield                                                   

The effective yield of a 3% account compounded monthly is (1+.03/12)12 – 1 = .0304 = 3.04%.

This means that a 3% account compounded monthly actually yields 3.04% at the end of the year.

 

With continuous interest, it’s .  Ex:, r = 6%, ieff = 6.184%.

 

Future Value of an Ordinary Annuity         

Ex:

$200 put into an annuity each month for 18 years at 16% annual growth compounded monthly will have

$247,176.82.

Monthly Payment on an Amortized Loan  

Ex:

If you buy a house for $125,000 at 8% compounded monthly for 30 years,

MP = $917.21, not including taxes, escrow, etc.

Total payment of the house would be 360 of these payments = $330,195.60.

Total interest would be the difference, = $205,195.60.

 

Decay of the Dollar, Inflation                                         FV = Pert

 

Ex:

What will $4000 be worth 32 years from now assuming a 4.1% inflation rate?

FV = 4000*2.71828 -.041X32 =$1077.12

 

Perpetuity                                                                           

Money in an account produces interest, and if you take that interest out each month to live on, then you have a perpetuity.  If $250,000 is in an account growing at 9% interest, then it will produce monthly payments back to you of 250,000(2.71828 .09/12 – 1) = $1882.05 per month.                      

 

 

Tips on Investing in Annuities

0]            Start NOW.  Start yesterday if you can go back in time and start it.

1]            Diversify.  Allocating your portfolio into a variety of fundings will protect you from type-specific crashes.

2]            Invest for the long-term, don’t react too harshly to temporal fluctuations.

3]            Analyze your allocations twice a year.

4]            Increase your funding by more than the rate of inflation, typically 4.1% per year, regardless of earnings increase/decrease/equality.

5]            Stay out of savings accounts, credit unions, focus toward CDs, mutual funds, tax deferred annuities, IRAs and other higher growth funds. Watch out for administrative expenses.

6]            More day traders lose than win.  Day traders pay commission when buying and when selling.

7]            Mutual funds reallocated will create capital gains, whose profits between funds are taxed at 20% F.I.T.

8]            Over-funding home loans will reduce the length of time the loan exists and the amount of interest paid dramatically.  However, if you over-fund a high yielding annuity rather than the home loan, then at any given moment in the future the amount of money you have in the annuity will exceed the amount of money you will have saved over-funding the home loan.  Bottom line: over-fund high rate annuities before home loans.  One reason to over-fund the home loan is the security of knowing you don’t owe money on the home, as well as the fact that annuities do have risk and the home loan doesn’t.

9]            An annuity’s doubling rate is very close to the Rule of 72 (Rule of 69).  The number of years an annuity takes to double is nearly 72 divided by the interest rate.  Ex: a 9% annuity will double in 8 years, a 6% annuity will double in 12 years, a 3% annuity will double in 24 years.  This is why savings accounts are poor investments, along with the fact that their interest is lower than inflation and you actually lose money.

10]          As you get closer to the end of your life your investments should progress from high yielding, high risk toward lower risk funds.  You don’t want to lose it all when you’re 71 years old.  Losing it all at 32 years old isn’t the end of the world (although it will seem like it at the time).

11]          An annuity converts to a perpetuity when you retire.  Aim your portfolio to act as a perpetuity you can live with in the future.

 

 

Savings accounts vs. Mutual Fund Annuities

Let’s look at putting $1000 a month in two accounts for 20 years, one at 2.5% (typical savings account) and

one at 12% (typical mutual fund).  Both are compounded monthly.

Future Value of an Annuity is .  For savings account, S=1000*310.9747

 

= $310,974.71.  Sounds like a lot?  It’s not.  In 20 years, $310,000 will only seem like 310,000e -.041*20 =

$137,000.   Now let’s put the money in a mutual fund.  In 20 years, S=1000*989.2554= $989,255.37,

which will seem like $436,000.  Both accounts had a funding of $240,000, so the savings account made

$70,974.71 while the mutual fund made $749,255.37.  The mutual fund made nearly 11 times as much

money as the savings account.  Which would you rather retire with?

 

Here’s one:  $500 a month into a 12% annuity for 43 years, only increase the input by 5% per year.

 

 

 

 

 

Increasing Funding on Annuities

 

Since inflation exists, funds are not worth as much as they would be if inflation didn’t exist.  A fund that builds up to a million dollars in 17 years will only seem like half a million dollars when you’re there.  A gallon of gas 30 years ago was only a quarter, 30 years from now it will be extremely expensive by today’s standards.  To deal with this an investor needs to increment their fundings accordingly.  Historically, inflation averaged 4.1% per year (based on the 20th Century). If you increase your funds by 4.1% per year, then you are increasing the money you invest now to resolve inflation.  However, you are not helping the money that has already been invested.  That’s why I recommend increasing at a rate much higher than inflation.  The extra moneys will help out the money that has already been invested.  Increasing your funding by 10 to 15 percent per year will trim up both inflation for today’s investments and yesterday’s investments.  Increasing your investments as a result of pay raises is not as wise.  Your pay raises probably won’t meet inflation rates.  Also, when you are retired your pay raises isn’t what will be feeding you, it will be your investment fundings, which will be a perpetuity at the time you use them.

 

Aiming For Your Perpetuity

 

Let’s say you think you can live on $2000 per month by today’s standards if your house payments are gone, kids are gone, etc.  If you plan on retiring in 47 years (you’re 18 now, and will retire at age 65), then first you must compute inflation. If you want the equivalent of $2000, which will be much more than $2000, you will have to have 2000e .041X47 = $13,737.74, or rounded off, $14,000 per month.  That sounds like a lot of money, but it’s only the same as $2000 today.  Your perpetuity must be able to do two things.  It must be able to give you $14,000 per month 47 years from now, and it must be able to increase how much it gives you later than that as a result of inflation.  Your perpetuity must also grow or you will run out of money when you least need to run out of money, when you’re too old to go out and work.  Starting with just the target of $14000 per month, let’s see how much you need.  When you are old, you will be in a safer growth rate, most likely around 7%.  So, $14,000 = P(ert – 1) where t = 1/12 (1 month is 1/12 of a year).  $14,000 = P(2.71828 .07/12 – 1 ) = P * .00585.  Solving for P, we get P = 14,000/.00585 = 2.4 million dollars.  Bottom line, if you have 2.4 million dollars in an annuity when you are 65 years old and that annuity grows at 7%, then it will produce $14,000 per month for you to live on in perpetuity.  As you take $14,000 out per month, the annuity will remain at 2.4 million dollars.  If you increase this amount by 15%, then you will have more money than the perpetuity needs to produce $14,000 per month, and the annuity will continue to grow even as you remove money.  15% added to 2.4 million dollars is 2.76 million dollars.  This amount of money will allow you to perpetuitize $14,000 a month to live on, and it will grow at a rate that will allow you to perpetuitize more money as inflation grips you as time rolls by.  So, the trick is to aim for a portfolio that has the amount of money and the interest rate necessary to fund your perpetuity.  A good interest rate goal is 7%, which is the typical CD rate.  You will do better, but it's a safe place to start for a worst case scenario.  The future value for an ordinary annuity is .  Let's follow the example from the above problem.  You want 2.76 million dollars, let's round that off to 3 million dollars.  A typical CD rate is 7%, k = 12, and t = 47.  That means that

.  Make it $700 per month.  More won't hurt.  This is the arithmetic if you make the same payments per month for 47 years, which is not going to be the case.  You will be incrementally increasing your payments as you go by 10 to 15 percent per year.  Your wealth is up to you.  The Big Macs you eat today could have been millions that you have tomorrow.                                                                                                                                        

Home Loan extra payments

At the beginning of an amortized home loan nearly all of the payment is in interest.  As the loan progresses, the amount of interest per payment decreases and the amount of principal per payment increases.  By your last payment, nearly the entire payment is principal and nearly nothing is interest.  Half way through the loan (15 years into a 30 year loan) one might assume that half the house is paid, only to be surprised when they find out they owe nearly as much for the house as they did the day they bought it.  If you would like to pay the house off in 15 years you can match principal with extra payments.  Let’s assume that your house payments have been amortized to $1000 per month.  It may be the case that $960 of that payment is interest and $40 is principal.  On the next payment you might have $955 interest and $45 principal.  So, in two months time you have paid $2000 for your house but only paid $85 toward the principal.  If you were to match principal each payment, then you first payment would be $1000 plus an additional $40, and your second payment would be $1000 plus an additional $45.  If you continue this throughout each payment you will eventually have matched principal for 15 years and will have paid off the house.  In addition to that your interest would have been decreased dramatically since they can’t charge you interest on money you don’t owe, making the time to pay off the house less than 15 years.  The savings are incredible.  A CPA will be able to analyze problems you might experience with tax and home loan over-funding rather than mutual fund over-funding.  But, if all you are interested in is getting the house paid off, this is the ticket.

 

Wealth Accumulation

People have assets and liabilities.  Assets are things that make you money, liabilities are things that cost you money.  Ultimately, you want the money the annuities make not to be used in buying things (liabilities) but rather be used to buy assets.  Buying assets will make you more money, which can then be fed into your asset-profit acquisition cycle.  For example, when you get money made from an asset, using it to buy a boat terminates the process with that money, whereas using that money to buy a 16% tax lien certificate will make that money make more money.  No matter how much you deny it, a boat is a liability if you are not using it to make money.  It is not an investment, and neither is a cool car, cool game, cool bike, cool CD, etc.  Honesty to yourself in these matters is difficult.

 

If you have a job, use as much of your paycheck as possible to fund either an annuity, a business, or real estate that can be rented and later sold for a profit.  All the money that comes in from these investments need to be turned into other investments, and any that are sold need to be reinvested into other assets.  The geometric growth of this system is awesome.  Furthermore, treat it like a business, form an LLC, and that allows you to convert your tax game with the following model:

 

Individual                                                                                             LLC

1]            Earn                                                                                       1]            Earn

2]            Tax                                                                                         2]            Spend/Use/Invest

3]            Spend/Use/Invest                                                                                3]            Tax

 

This brings your taxable amount to a much lower quantity, possibly zero.  Keep in mind that 50% of your earnings go away in taxes.  Most people think that IRS is your largest tax, but it isn’t, it’s your Social Security.  You pay 7.5%, your employer pays 7.5%.  You might think that you didn’t pay that, they did, but in fact, it was with money that would have been yours had they not had to take that money out.  So, you are taxed 15% from your gross.  IRS, Soc Sec, etc, all taxes put together usually amount to at least 50%, and it can be radically reduced.

 

When selling a rental property for profit, you can avoid capital gains taxes by reinvesting that money into a larger rental investment property through section 1031 of the IRS Code.   This method allows you to escalate your property without ever being taxed until you finally convert it into money.  Money that is not working to make money turns itself into a liability.  Always reinvest.  When buying things, ask yourself  if it an asset or a liability.  Most Americans buy things that they think are assets but are actually liabilities.  A life-long training is required.  Annuities         Real Estate           Asset Acquisition Cycle