A Quick Market Newsletter

A short post tonight.  Here is a link to a useful free financial newsletter from Axiom Financial.  The format has remained the same for several years and provides a quick weekly update of market conditions.


Image from Axiom Financial

Image from Axiom Financial


Compound interest and doubling your money

There are some basic rules of finance whose understanding is integral to the proper management of money.  The first rule has been to understand the concept of the time value of moneyInterest rates drive all things finance; from credit card debt and house buying to savings accounts and bond investments.  The concept of the time value of money is rooted in mathematics and can be cumbersome to commit to memory.  The good news is that there has long been a rule that is easy to commit to memory and serves as the 95% solution to figuring out how much an asset can make you or how much a loan can cost you.

The rule is called “The divide by 72 rule“.  If you already know of this rule, you’re ahead of many.  However, do you know why that rule works, or even whether it actually does or not.  Anything based math should not be taken on faith, but instead proved through relationships.  The 72 rule states:

To quickly calculate the time in years to double your money in an investment due to compounding interest payments, divide 72 by the annual interest rate.  For example an 8% interest rate would take (72/8) 9 years to double the money invested.

This can work with interest rates that are compounded annually or even in shorter terms, so long as the annual effective rate is used in the calculation.

Rate Rule of 72 Annual Delta %
1% 72.0 69.7 3.2%
6% 12.0 11.9 0.9%
11% 6.5 6.6 -1.5%
16% 4.5 4.7 -3.8%
21% 3.4 3.6 -6.1%
26% 2.8 3.0 -8.3%
31% 2.3 2.6 -10.5%
36% 2.0 2.3 -12.7%

>>>The above table shows a comparison between the rule of 72 and annually compounded interest rates.  Notice that the error is low for interest rates that we commonly calculate.  The formula for the time to double your money is Time=ln(2)/ln(1+rate), where the time is in years and the interest rate is expressed as a percentage.  The divergence at higher interest rates from the rule of 72 is cause by the rule of 72 actually being tied to the formula for continuously compounding interest.  This is where interest is always compounding upon itself.  The formula for doubling you money in this case in Time=ln(2)/rate.  This formula tracks perfectly with a rule of 69.3 as shown below.  The reason that 72 is used is because “head math” with 72 works easier as 72 has plenty of multipliers (1,2,3,4,6,8,12…and so on) that are common interest rates.

Rate Rule of 69.3 Annual Delta %
1% 69.3 69.3 0.0%
6% 11.6 11.6 0.0%
11% 6.3 6.3 0.0%
16% 4.3 4.3 0.0%
21% 3.3 3.3 0.0%
26% 2.7 2.7 0.0%
31% 2.2 2.2 0.0%




How does an annuity work? What determines your monthly payment?

Good Evening FPO Readers,

An annuity is a financial instrument which can be purchased with a lump sum payment.  In return, the annuity pays a monthly payment to the annuity holder for the remaining life of the annuity.  The payment can be either at a fixed or variable rate and the remaining life can be defined multiple ways, but is most commonly based on the remaining physical life of the annuity holder; and their spouse in the case of a joint annuity.  Since the life of the annuity is tied to your own lifespan, an annuity is more properly classified as an insurance product as opposed to an investment product.  Even though an annuity wraps together both an investing and an insurance element it is possible to break the two apart for analysis.

The below explanation is for a standard, fixed rate annuity.  There are various types of annuities, but the underlying principles described below remain the same.

Think of an annuity as a combination of a long term bond and a reverse cash flow life insurance policy at 0% interest.  What is a reverse cash flow life insurance policy you ask?  It is the same as a normal life insurance policy, but the order of payments switch.  The lump sum is paid up front by you and the monthly payments are paid afterwards to you for the rest of your life.  The opposite of your life insurance policy, right?

The bond element is mostly straightforward.  In the case of a $100K annuity, the bond element would consist of a $100k bond that pays the current market rate for long term, low risk bonds, which is about 1.75% presently.  In this case, the annual simple interest payment would be $1750.

The reverse cash flow life insurance is based on the age of the annuity holder at the time of annuity issue.  The $100k lump sum is exchanged for monthly payments for the rest of your life.  If you live a long time, you come out ahead, otherwise the issuer of the annuity comes out ahead.  The rate of the insurance component is based on market rates, but for a 65 year old man expect a yearly payment of about $4500.

The total annuity payment is $6250 per year or about $521/month.

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