Simple vs. compound interest rate

 1.      Simple annual interest rate 

The annual interest pays to holders is a constant every year. The common scenario is guarantee investment certificate, GIC, offered by banks. 

Assuming that we purchased $10,000 GIC with 10% annual interest for 10 years from a bank. What will we get by the end of 10 years? 

Yearly interest would be $10,000 * 10% = $1,000 (we would get $1,000 per year)

After 10 years, the interest portion would be $1,000/year * 10 years = $10,000 

We will get $10,000 (initial capital) + $10,000 (interests) = $20,000 as a lump sum payment from the bank. 

2.      Compound interest rate 

FV = PV (1 + r/n)^nt 

FV       =          final amount, future value

PV       =          initial principal balance, present value

r          =          interest rate

n          =          number of times interest applied per time period

t           =          number of time periods elapsed 

Most of time we are dealing with annual compound interest rate, i.e. interest payment once per year (n=1). The formula would be simplified as follows 

FV = PV (1 + r)^t 

Consider this simple example, we are investing in a security (stock)  that pay 10% annual dividend, which is re-invested in this security. 

Year 1, our investment would be $10,000 + $10,000 * 10% = $11,000 (the interest portion is $1,000 by end of year 1) 

Year 2, our investment would be $11,000 + $11,000 * 10% = $12,100 (note that $1,000 interest in year 1 was used in year 2 to generate interest portion) 

By using the formula above, at the end of year 10 our investment would be 

FV = $10,000 (1 + 0.1)¹⁰ = $25,937.42 

By comparing both examples in #1 and #2, compounding interest rate is very powerful. 

The percentage gain would be (25,937.42 – 20,000) / 10000 * 100% = +59.37% more with compound interest rate after 10 years. 

Author: Vinh Nguyen, B.Eng.

Email: canvinhgmail.com