About Me

In writing the "About Me" portion of this blog I thought about the purpose of the blog - namely, preventing the growth of Socialism & stopping the Death Of Democracy in the American Republic & returning her to the "liberty to abundance" stage of our history. One word descriptions of people's philosophies or purposes are quite often inadequate. I feel that I am "liberal" meaning that I am broad minded, independent, generous, hospitable, & magnanimous. Under these terms "liberal" is a perfectly good word that has been corrupted over the years to mean the person is a left-winger or as Mark Levin more accurately wrote in his book "Liberty & Tyranny" a "statist" - someone looking for government or state control of society. I am certainly not that & have dedicated the blog to fighting this. I believe that I find what I am when I consider whether or not I am a "conservative" & specifically when I ask what is it that I am trying to conserve? It is the libertarian principles that America was founded upon & originally followed. That is the Return To Excellence that this blog is named for & is all about.

Sunday, July 30, 2017

Compound Interest Quiz

Thanks to everyone who sends me quizzes they think the readership would enjoy.  I've got them all & will post selected ones from time to time throughout the year.  Please keep them coming.
Please solve the Compound Interest Quiz below. 
I remember a life insurance salesman who regularly called on my father when I was a young boy talking about "the magic of compound interest" – which is illustrated in the quiz below.
Please let me know how you work the problem.  I will post all correct answers or alternatively will send the solution privately to anyone who requests it if no one figures it out.
Compound Interest Quiz
If something is growing 100% per annum, how much does it grow every six months?


  1. I'm sure it has something to do with the Rule of 7's. All I want to know is what is growing at 100% per annum!

  2. I tried a couple examples but could not calculate the right answer. If I tried this one doubt it would be right.


    1. I will try this: Annual growth of 10% in six months - $1000 will be worth $1074.16.

      Solution: 10% a year will be 1.2% per month which comes to $1074.16

      I think I am pretty close.

    2. The $1000 needs to become $2000 in one year (& then $4000 the next year etc.) so your 10% is very low. Remember that 100% per annum means that the principal doubles. Will send the answer out after I hear from a few others. Keep trying using these hints – you are right, it is stimulating.

    3. OK trying again, $1000 annual income of 100% for 6 months,

      100% divided by 12 months is 8.3% per month

      1613.50 in 6 months am I close?

    4. You are getting closer. What your work says mathematically is that the 6 month rate is 61.35% based on a monthly interest rate of 8.3%. $1000 will become $1613.50 in 6 months which is correct as far as the math goes @ an 8.3% monthly compound interest rate. But that will result in the $1000 being worth $2603.40 in one year which is higher than the specified rate of $2000 in one year meaning that 8.3% per month or 61.35% in six months is too high. Back it down a little. You can use your method of trial & error by checking it – when you calculate the six month rate see if you get $2000 @ the 1 year mark. When you do you know you have it. I will show you how to do the problem without trial & error.

      I am impressed with your work & for trying so hard.

    5. Thanks for the answer for compound interest, now to find one with 8%.

  3. A brute-force solution:


    1. 100% per annum means that the amount doubles in 12 months.
    2. Interest is paid monthly.

    Define y = Monthly increase multiplier = 1 + (monthly % rate)

    Start with $1.00
    After 1 month, balance = 1*y = y1
    After 2 months, balance = (1*y)*y = y2
    After 3 months, balance= (1*y)*y*y = y3
    After 12 months, balance = y12 = $2.00

    Cranking the algebra:

    y12 = 2

    (y12)1/12 = (2)1/12
    y = (2)1/12

    Using a calculator:
    y = 1.059463094

    The monthly rate of return is therefore: 5.9463094%
    After 6 months, balance = 1*y6 = 1*(1.059463094)6 = $1.41

    Answer: ~41%

    1. Congrats PRu. A fine job.

      A less brutal force would have just taken (1+X)2 = 2 squaring both sides gives 1+X = 2.5 = 1.4142

      X = .4142 or 41.42% in six months

      the simplifying point is to make the compounding period 6 months instead of the conventional 1 year

      BTW - the software on the blog does not let the exponent show up clearly in either the PRu solution or mine e.g., 2.5 really means 2 to the 1/2 power or the square root of 2 which = 1.4142

    2. Second part of second line should read “(1+X)2 = 2 taking the square root of both sides gives 1+X = 2.5 = 1.4142” Sorry for the typo.

  4. Doug,

    According to my calculations through trial & error, I came up with an annual rate of approx. 83 % compounded semiannually using $100 invested: 100( 1.415) ^2 = 200.22 after 1 year and 100(1.415)^ 4 = 400.89 after 2 years.

    Still trying to figure it algebraically.

  5. Solution 1: Using compound interest formula:
    Compounded value (C)=P(1+r)*n where P is principal or initial sum, r=rate per period and n is number of periods.
    But C = 2P
    Therefore 2P = P(1+r)*2, and dividing both sides by P results in
    2 = (1+r)*2
    so, sq. root 0f 2 = 1+r.
    i.e. 1.4142 = 1+r
    r = 1.4142 - 1 = 0.4142 or 41.42%

    Solution 2: Using approximation compounding rule of 72, maximum semiannual interest rate is .36, which when compounded does not double the original sum.
    Using trial and error and stepping up the rate in the above mentioned formula to .40, .41, .42 achieved doubling of the original sum with a rate of 41.42%

  6. Compound interest quiz - just looking, off the top of my head, is it 50% (assuming no other deposits have been made)?

    1. 50% every six months will double the principal in only the first year using simple interest – the problem is to figure the six month compound interest rate for every year that keeps on doubling. Using 50% simple interest yields only 3 the second year instead of 4 & falls further behind every year like with 4 the third year instead of 8. If you use 50% compounding you get more than a doubling in the first year = 2.25. So no, 50% is not the answer any way you try to figure for the reasons shown. Hope these hints help.

  7. I worked on the compound interest question and strictly by trial and error I am coming up with $1414.05