I was in high school when I figured out that I could not save enough to buy a car. So I didn’t buy one. It was not until our three kids finished high school that we actually got more done than just letting savings be a thing of interest.
Are first real savings was having our first house paid for before the first kid went off to college. We never rented again.
Now we are renting an apartment in a residential care site. I have yet to figure out just what justifies the monthly payment. Selling the house came first. So now I need to review short term (simple interest) and long term (compounded interest) as a background for understanding the way monthly annuity payments are calculated that will help pay our residential care bill.
Annuity calculators on the Internet produce different results. In general, an expected annuity payment of $2000/month for 10 years certain requires a pot of money in cash around $224,000. Now $2,000/month for 10 years is a total of $240,000. The total profit is only $16,000 or $1,600/year when removed each year and not reinvested.
The rate of 0.0071 or 0.71% [($16,000/$224,000)/10 years] simple interest must be adjusted to the fact that the insurance company is only holding the full pot on the first month and holding an empty pot after the last month. On average the company is holding half of the pot. The resulting interest rate is then twice that above [($16,000 to me/$112,000 average pot)/10 years] or 0.014 or 1.4% on average. That is $130.67 interest ($112,000 x 1.4%) and $1869.30 principal is in, on the average (fifth year), annuity payment of $2000.
The annuity returns our money in even monthly payments, Add annuity payments to SS and MO pension and we expect to have the residential care bill about paid each month for 10 years if we ignore inflation.
Can we do better managing the money ourselves? CDs are currently paying 0.7% or 1/2 the rate of 1.4% from the insurance company. Only CDs are government insured.
The insurance company, holding the annuity, is reinvesting the interest each year (compound interest). The first few years, I found, show a straight line characteristic of simple interest (Chart 13).
The difference between simple and compound interest is therefore very small in the short term..
Long term holdings average out financial bumps plus long term adds the earning power of compounding for the insurance company.
In summary, we can do the compounding calculations on the principal each payment, or, on the interest rate and the starting pot (Chart 15). At 1% it takes five years to gain a dollar on a $1,000 CD by compounding the interest. Compounding by year (Principal x Rate x Year) yields the same return as compounding the rate [Pot * ((1 + rate)^Year) -1]. It is this last formula for compounding by interest rate that I need to make sense of annuities.