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Interest Rate Equation Conversion Formulae
This page lists Interest Rate Equations to use when converting between different Nominal and Effective Interest Rates.
INTEREST RATE CONVERSION FORMULAE
GENERAL INTEREST RATE FORMULA
i = Effective Annual Interest Rate
NOMINAL ANNUAL COMPOUNDED SEMI-ANNUALLY (NACSA) FORMULA
NOMINAL ANNUAL COMPOUNDED QUARTERLY (NACQ) FORMULA
NOMINAL ANNUAL COMPOUNDED MONTHLY (NACM) FORMULA
NOMINAL ANNUAL COMPOUNDED DAILY (NACD) FORMULA
EXAMPLES: INTEREST RATE CONVERSION FORMULAE
OUR GIVEN ANNUAL EFFECTIVE RATE
For this example let's assume that we are given an Annual Effective Rate of 10% to convert to various other Nominal and Effective Rates.
So we are given:
i = 10% = 0.10
GENERAL INTEREST RATE FORMULA
NOMINAL ANNUAL COMPOUNDED SEMI-ANNUALLY (NACSA) FORMULA
NOMINAL ANNUAL COMPOUNDED QUARTERLY (NACQ) FORMULA
NOMINAL ANNUAL COMPOUNDED MONTHLY (NACM) FORMULA
NOMINAL ANNUAL COMPOUNDED DAILY (NACD) FORMULA
SUMMARY TABLE
| Interst Rate Type |
Abbreviation |
Symbol |
Value |
| Effective Annual Rate |
NACA |
 |
10.00% |
| Nominal Annual Compounded Semi-Annually |
NACSA |
 |
9.76% |
| Nominal Annual Compounded Quarterly |
NACQ |
 |
9.65% |
| Nominal Annual Compounded Monthly |
NACM |
 |
9.57% |
| Nominal Annual Compounded Daily |
NACD |
 |
9.53% |
NOTE: As you go down the Table above the Nominal Rates decrease (i.e. as the compunding intervals increase (n becomes bigger) the nominal rates decrease).
BASIS POINTS
BASIS POINTS DEFINED
|
100 |
Basis Points |
= |
1% |
| OR |
100 |
Basis Points |
= |
0.01 |
| Therefore |
1 |
Basis Point |
= |
0.0001 |
| OR |
1 |
Basis Point |
= |
0.01% |
To express Basis Points as a percentage you simply multiply the given Basis Points by 0.0001 (= 0.01%)
EXAMPLES - BASIS POINTS
| 10 |
Basis Points |
= |
0.0010 |
= |
0.10% |
= (10*0.0001) |
| 20 |
Basis Points |
= |
0.0020 |
= |
0.20% |
= (20*0.0001) |
| 50 |
Basis Points |
= |
0.0050 |
= |
0.50% |
= (50*0.0001) |
| 100 |
Basis Points |
= |
0.0100 |
= |
1.00% |
= (100*0.0001) |
| 150 |
Basis Points |
= |
0.0150 |
= |
1.50% |
= (150*0.0001) |
| 500 |
Basis Points |
= |
0.0500 |
= |
5.00% |
= (500*0.0001) |
| 1000 |
Basis Points |
= |
0.1000 |
= |
10.00% |
= (1000*0.0001) |
| 2000 |
Basis Points |
= |
0.2000 |
= |
20.00% |
= (2000*0.0001) |
| 3000 |
Basis Points |
= |
0.3000 |
= |
30.00% |
= (3000*0.0001) |
| 5000 |
Basis Points |
= |
0.5000 |
= |
50.00% |
= (5000*0.0001) |
DESCRIPTIVE EXAMPLES
EXAMPLE 1.
The Reserve Bank has increased the official REPO rate by 50 Basis Points to 8.5%. What was the REPO rate before the increase?
SOLUTION:
Let's first express the Basis Points as a percentage
50 Basis Points = 50*0.0001 = 0.50%
So the REPO rate increased by half-a-percent
So the original REPO rate was = 8.5% - 0.5% = 8.0%
(REPO rate is the interest rate at which Central/Reserve Banks lend to Commercial Banks.)
EXAMPLE 2.
The effective discount rate on Government Bonds increased from 9.5% to 11%. By how many Basis Points did the Public Service Treasury increase the discount rate?
SOLUTION:
(a) Let's first calculate the difference between the two rates:
Difference = 11% - 9.5% = 1.500%
(b) Now let's convert this difference to Basis Points:
Percent = 1.500% = 0.0150
Basis Points = 0.0150/0.0001 (0.0150 divided by 0.0001) = 150.
So The Treasury increased the Discount Rate by 150 Basis Points.
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