Today, the account manager of a bank came to sell an “incremental whole life insurance”, claiming to be able to lock in a 3.5% rate of return.
Specifically, it means investing a sum of money every year in the first 5 years without accruing interest, and starting to accrue interest at a rate of return of 3.5% in the 6th year.
Moreover, the income of financial management is not high now. It seems that it is not bad to be able to lock in the interest rate of 3.5. Although no interest is calculated in the first 5 years, intuitively it seems that the interest rate will not drop too much.
However, upon careful calculation, I found that this is not the case at all.
Assuming the interest rate is x, according to the summation formula of the proportional series, we can know that the amount in the 5th year should become =(1-x^5)/1-x=, so you can get the equation ~(1-x^5)* x/(1-x) = 5*1.035~.
For a math scumbag like me, this formula can’t be calculated at all, but fortunately I have Emacs [[help:calc][calc]]
So, let’s run =Mx calc=, input =’fsolve((1-x^5)*x/(1-x) = 5*1.035,x)= to get the result as follows:
#+begin_src calc :export both :results org
fsolve((1-x^5)*x/(1-x) = 5*1.035,x)
#+end_src
#+RESULTS:
#+begin_src org
x = [0.999999999998, 1.01148914259, (-1.29523147819, 0.862841415432), (0.289486906893, -1.42424965717), (-1.29523147819, -0.862841415432), (0.289486906893, 1.42424965717)]_n4
#+end_src
It can be seen that the evaluation value of x is =1.01148914259=, which means that the actual rate of return is only less than =1.15%=, which is really different from the intuitive feeling.
This article is reprinted from: https://lujun9972.github.io/blog/2022/08/10/%E4%BD%BF%E7%94%A8-calc-%E8%AE%A1%E7%AE%97%E4 %BF%9D%E9%99%A9%E5%AE%9E%E9%99%85%E6%94%B6%E7%9B%8A%E7%8E%87/index.html
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