Annuity Annual Accrual

A customer recently asked how to use TValue to determine the balance and annual interest contributions if they invested $100,000 in an annuity that was compounded annually for 15 years.

Compound interest is interest earned or paid on both the principal sum and the earned interest of any investment or loan. Basically, it is interest on interest. It is most often used when reinvesting the interest earnings back into the original investment. I thought this would be a great exercise in TValue to show the impact on compounding year to year over a length of time.

In TValue, we used Annual compounding and a Nominal Annual Rate of 5%. On Line 1, we entered an Invest event for 100,000. On Line 2, we entered $0 payments, with the Number 14 and Annually. When you enter $0 payments in TValue, the software will show you the interest accruing and the interest will get added to the principal as it is compounded. When you have compound interest, it will show you the interest growth year to year as you are earning interest on interest.

When you do this exercise, you end up with a balance in year 15 of $207,892.83. The interesting part is how the interest grows from year to year due to compounding. In year 1, the interest is $5,000. In year 15, the interest is $9,899.66, almost double the annual contribution.

Here are a couple classic quotes from Albert Einstein who was a fan of compound interest:

• “Compound interest is the eighth wonder of the world. He who understands it, earns it ... he who doesn't ... pays it.”
• "The power of compound interest, the most powerful force in the universe."
• "The greatest mathematical discovery of all time".

This is a great concept to understand.