Compund Interest Calculations

 

A key skill I would have loved to have learnt while I was in high school was understanding interest rates and the difference between simple and compound interest. Particularly simple interest in relation to loans, but being able to compare simple and compund interest for savings gains.

The calculations for simple and compounding interest are very different and result in very different monetary outcomes as shown in the graph below. Learning key differences, I think would have helped me learn how to save/invest money for the biggest gains earlier in my life.

(CFI Team, 2022)

Compound Interest:

This is a type of interest which changes (not fixed). It uses the principal amount and the pervious interest to calculate the new interest. They often call this ‘interest on interest’. Therefore, as interest gets added to the total principal, the new interest is calculated based on this larger number which in turn, increases the interest for the next period.

 

The formula for compound interest is A = P(1 + r/n)^nt.

A = future value (Principal + interest)
P = principal balance
r = interest rate (decimal form)
n = number of times interest is compounded per time period
t = number of time periods (years)

 

Example: I invest $15,000 at an annual interest rate of 3.5%, compounded monthly. After 5 years the value will be…

P=15000
r=0.035
n=12
t=5

A = 15000 x (1 + 0.035 / 12) ^ (12 x 5)

A = $17,864.14

 

This outcome is obviously very beneficial in terms of increasing the total principal, gaining more money quickly in my savings.

 

Simple Interest:

What I did not understand for years was the difference between this and simple interest, which is where majority of my money was sitting. Again, referring to the graph above, the gains are smaller in comparison, as there is no compounding on the interest. In simple interest we do not need to use ‘n = number of times interest is compounded per time period’ for this reason. This means the interest is only calculated on the principal amount, rather than the principal with the additional monthly interest. The difference can be seen when comparing the compound interest example above, to if it only used simple interest.

 

The formula for simple interest is: I = Prt

I = simple interest total
P=15000
r=0.035
t=5

I = 15000 x 0.035 x 5

I = $2625.00

To compare the simple interest income total after the 5-year period to compounded interest, we add the interest to the principal amount.

Simple Interest on investment = $17,625.

 

Comparing these two outcomes, I am better off investing with compounding interest as this will increase my investment by $239.14.

 

Reflecting on these formulae, the calculations are really just basic algebra and not too hard to understand once you know the different components to the equations. It is just a substitution equation with multiple components which in reality can frequently change. Over the last few years, we have seen large changes in interest rates and how this can positively and negatively effect investments. Completing the calculations myself on my own savings has really helped my understanding and financial literacy in relation to simple and compounding interest. Previously when speaking to people at the banks, I was always so intimidated and lacked the understanding of interest and the rates they would explain. But really, it can be broken down and simplified for everyone to understand, so they can make the best financial decisions for themselves. This can have significant positive impacts for people’s savings, superannuation and other investments.

 

Reference List:

CFI Team. (2022). Types of Interest. Corporate Finance Institute. Retrieved 12/11/22 from https://corporatefinanceinstitute.com/resources/commercial-lending/types-of-interest/

Hazell, A. (2022). Compound Interest Formula with Examples. The Calculator Site. Retrieved 9/11/22 from https://www.thecalculatorsite.com/finance/calculators/compound-interest-formula.

Pournara, C. (2013). Teachers’ knowledge for teaching compound interest. Pythagoras, 34(2), 1-10.

Song, C. (2020). Financial illiteracy and pension contributions: A field experiment on compound interest in China. The Review of Financial Studies, 33(2), 916-949.