Lesson 1, Topic 1
In Progress

1.9. Effective and nominal interest rates

ryanrori January 25, 2021

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Make sure you study offers by lenders very carefully before making a decision on which account to invest your hard-earned money, or from whom to borrow.  Important questions to ask are:

  • What interest are you going to charge?
  • What are the costs involved?

When you invest money, the lenders promote effective interest rates, but when you borrow money, they stress the lower nominal interest rates:

  • Effective interest rate – The effective interest rate includes the effect of compound interest. Compound interest is when you earn interest on top of interest by reinvesting the interest.  For example:

If you invest R100 @ 10% per year, and interest is compounded monthly, your R100 would become R100.83 after 1 month:

R100 capital + interest of R100 x 10% x 1/12

At the end of the 2nd month, it would be R101.67: 

R100.83 capital x 10% x 1/12, and so on

After 12 months it comes to R110.47.This means that you have earned an effective 10.47% in interest and not 10%.

Example:

World bank offers John an investment opportunity recurring a minimum balance of R3000. In its advertising it offers an interest rate of 15% p.a. compounded monthly the effective interest rate is:

= {1 +  (rm/m}ⁿ – 1

= { 1 + (0,15/12)}¹² – 1

= 1,0125)¹² – 1

= 1,16075 – 1

= 16,0775%

  • Interest rates always take into account the inflation rate so that the rate of return on capital is profitable.
  • Nominal interest – Nominal rate or simple interest is based on the interest rate for a specific period of time. If you invest R100 at 10% a year, you will receive R10 for that year.  Simple interest can also be referred to as a flat rate of interest. 

Interest is calculated and added on at the start of the loan agreement; therefore, for the life of the loan, the interest is being calculated on the amount you originally borrowed. 

Car finance and loan sharks generally work on a flat rate of interest.

Example:

The nominal rate of return

M = {(1+ r) (1 + i)} -1

Where:

M=nominal rate of return

R=real rate of return

I =expected inflation rate

If a company requires an investment to earn a real rate of return of at least 6% and the expected inflation rate is 15,1%, then projects must provide a nominal return of at least 22%

M={(1.06)(1.151)}-1

  =0.22

The project’s cash flow will therefore be discounted at a rate of 22%. A 22% will protect the company against the loss in purchasing power and also provide a real return of 6%

To find real rate of return

R={(1+m)/(1+i)}-1

= 1 + 0. 22

  1 +  0.151       – 1

= 0,059

= 0,06  or 6%