# Working with Interest

Interest?  What is it, and who does it benefit?

Interest, in financial terms, is an amount of money earned on either (i) a savings account, (ii) an investment, or (iii) a loan.  In the first two cases, the interest earned benefits the person putting money into the savings account, or making the investment.  In the third case, the interest earned benefits the person (or institution) providing the loan or line of credit.  For example, you may deposit money into your savings account at the bank each month, and receive 2% per annum (pa) interest.  Or, you may have a credit card which is charged 19% pa interest on the balance at the end of each month.  The ‘%’ symbol means “percent” and refers to “part of 100” (“per cent”).  For example, 2% is two (2) parts in 100, which as a fraction looks like 2/100, or as a decimal is 0.02.  “Per annum” (pa) means “per year”, referring to a 12 month period.

Interest is earned as either Simple or Compound, with the latter often being described as “Interest on Interest”.  Let’s look at an example to show the difference between these two types of interest.

Simple Interest is calculated via the formula:

I = Prn

Where:

I = the interest earned

P = the Principal (ie the original amount invested or borrowed)

r = the interest rate in percent

n = the number of terms (ie the number of repeated minimum time periods over which interest is earned)

Let’s use this formula to calculate the Simple Interest earned (I) on a \$4,000 savings account (P) over a one (3) year period (n), at 2% pa interest (r).

I = Prn

I = \$4,000 x 2/100 x 3

I = \$240.00

Therefore, the Interest earned on this savings account is \$240.00.

Compound Interest is calculated via a different method.  The first formula used is:

FV = PV(1 + r)n

Where:

FV = Future Value (ie the total value of the investment or loan at the end of ‘n’ time periods)

PV = Principal Value (ie the original amount invested or borrowed)

r = the interest rate in percent

n = the number of terms (ie the number of repeated minimum time periods over which interest is earned)

The Interest earned is then calculated via the formula:

I = FV – PV

Let’s use this formula to calculate the Compound Interest earned (I) on a \$4,000 savings account (P) over a three (3) year period, at 2% pa interest, calculated and paid monthly.  Note, that in this case ‘n’ = 36 (3 x 12), and ‘r’ = [2/100]/12, as the interest is calculated and paid monthly, and there are 12 months in a year.

FV = PV(1 + r)n

FV = \$4,000 x (1 + [2/100]/12)36

FV = \$4,247.13

Then,

I = FV – PV

I = \$4,247.13 – \$4,000

I = \$247.13

So, what’s the difference between Simple and Compound Interest?  Well, in this example, \$7.13.  Compound Interest earns \$7.13 more interest on the same Principal Amount invested.  And, while this may not look like much, consider this multiplied out over a 30 year, \$400,000 home loan.  The difference is amplified to \$88,483.59. 