Engineering Economic Analysis

• 
  
  
  
  • '-,- -_. .. --'..
  
  
  
  

Nominal and EffectiveInterest 111

If a savings bank pays 11/2%interest every 3 months, what are the nominal and effective interest

rates per year?

Nominal interest rate per year r=4 x 11/2%=6%

Effective interest rate per year ia=(1+ :) m- 1

(

0.06

)

4

= 1 +"4 - 1=0.061

=6.1%

Alternately,

Effective interest rate per year ia=(1 +i)m- 1

=(1 + 0.015)4 - 1=0.061

=6.1%

Table 4-1 tabulates the effective interest rate for a range of compounding frequencies

and nominal interest rates. It shouldbe noted that whena nominalinterestrate is compoundedI

TABLE4-1 Nominal and Effective Interest

Nominal Interest Effective Interest Rate per Year,i/lWhen

Rate per Year Nominal Rate Is Compounded

r(%) Yearly Semiannually Monthly Daily Continuously

1 1.0000% 1.0025% 1.0046% 1.0050% 1.0050%

2 2.0000 2.0100 2.0184 2.0201 2.0201

3 3.0000 3.0225 3.0416 3.0453 3.0455

4 4.0000 4.0400 4.0742 4.0809 4.0811

5 5.0000 5.0625 5.1162 5.1268 5.1271

6 6.0000 6.0900 6.1678 6.1831 6.1837

8 8.0000 8.1600 8.3000 8.3278 8.3287

10 10.0000 10.2500 10.4713 10.5156 10.5171

15 15.0000 15.5625 16.0755 16.1798 16.1834

25 25.0000 26.5625 28.0732 28.3916 28.4025