1. Time Value of Money
Simple Interest (
):
Compound Interest (
):
where
(rate per period) and
is total periods.
Effective Rate (
):
Future Value (Annuity Regular):
Present Value (Annuity Regular):
2. Equations, Matrices, & Series
Quadratic Equation Roots: For
,
Arithmetic Progression (
):
term
; Sum
Geometric Progression (
):
term
; Infinite Sum
(
)
Part B: Logical Reasoning (20 Marks)
Direction Sense: North (Up), South (Down), East (Right), West (Left).
Blood Relations: Use a family tree (Square/"+" for Male, Circle/"–" for Female).
Seating Arrangement: Clockwise = Left, Anti-clockwise = Right (for circular facing center).
Part C: Statistics (40 Marks)
1. Central Tendency & Dispersion
Mean (
):
Empirical Relation:
Standard Deviation (
):
Coefficient of Variation (
):
2. Correlation & Regression
Karl Pearson’s (
): Range
Spearman’s Rank (
):
Regression Equation (
on
):
3. Index Numbers
Laspeyres (
):
Paasche (
):
Fisher’s Ideal (
):
Here are the missing formulas filled in clearly.
1. Time Value of Money
Simple Interest
SI = PRT
where P = principal, R = rate per period, T = time.
Compound Interest
A = P\left(1+\frac{R}{100}\right)^T
where R is the rate per period and T is total periods.
Effective Rate
ER = \left(1+\frac{R}{m}\right)^m - 1
for nominal annual rate R compounded m times per year.
Future Value (Annuity Regular)
FV = A\left(\frac{(1+i)^n - 1}{i}\right)
Present Value (Annuity Regular)
PV = A\left(\frac{1-(1+i)^{-n}}{i}\right)
2. Equations, Matrices, & Series
Quadratic Equation Roots: For
ax^2+bx+c=0
the roots are
x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}
Arithmetic Progression (A.P.)
nth term:
a_n = a+(n-1)d
Sum of first n terms:
S_n=\frac{n}{2}\left[2a+(n-1)d\right]
Geometric Progression (G.P.)
nth term:
a_n = ar^{ n-1}
Infinite sum (|r|<1):
S_\infty=\frac{a}{1-r}
Part C: Statistics
1. Central Tendency & Dispersion
Mean
\bar{x}=\frac{\sum x}{n}
Empirical Relation
Mode = 3(Median) - 2(Mean)
Standard Deviation
\sigma=\sqrt{\frac{\sum (x-\bar{x})^2}{n}}
Coefficient of Variation
CV=\frac{\sigma}{\bar{x}}\times 100
2. Correlation & Regression
Karl Pearson’s Coefficient of Correlation
r=\frac{\sum (x-\bar{x})(y-\bar{y})}{\sqrt{\sum (x-\bar{x})^2\sum (y-\bar{y})^2}}
Range: -1 \le r \le 1
Spearman’s Rank Correlation
\rho = 1-\frac{6\sum d^2}{n(n^2-1)}
Regression Equation of y on x
y-\bar{y}=b_{yx}(x-\bar{x})
where
b_{yx}=r\frac{\sigma_y}{\sigma_x}
3. Index Numbers
Laspeyres Index
LPI=\frac{\sum p_1q_0}{\sum p_0q_0}\times 100
Paasche Index
PPI=\frac{\sum p_1q_1}{\sum p_0q_1}\times 100
Fisher’s Ideal Index
F=\sqrt{LPI \times PPI}
If you want, I can also turn this into a clean one-page formula sheet or fill the blanks exactly in your original format.
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Formula Chart
1. Time Value of Money
- Simple Interest: SI = PRT
- Compound Amount: A = P\left(1+\frac{R}{100}\right)^T
- Effective Rate: ER = \left(1+\frac{R}{m}\right)^m - 1
- Future Value of Annuity: FV = A\left(\frac{(1+i)^n - 1}{i}\right)
- Present Value of Annuity: PV = A\left(\frac{1-(1+i)^{-n}}{i}\right)
2. Equations, Matrices, & Series
- Quadratic Roots: x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
- A.P. nth term: a_n = a+(n-1)d
- A.P. sum: S_n=\frac{n}{2}[2a+(n-1)d]
- G.P. nth term: a_n = ar^{n-1}
- G.P. infinite sum: S_\infty=\frac{a}{1-r}, for |r|<1
3. Statistics
- Mean: \bar{x}=\frac{\sum x}{n}
- Empirical relation: Mode=3(Median)-2(Mean)
- Standard deviation: \sigma=\sqrt{\frac{\sum (x-\bar{x})^2}{n}}
- Coefficient of variation: CV=\frac{\sigma}{\bar{x}}\times 100
- Karl Pearson’s correlation: r=\frac{\sum (x-\bar{x})(y-\bar{y})}{\sqrt{\sum (x-\bar{x})^2\sum (y-\bar{y})^2}}, range -1 to 1
- Spearman’s rank: \rho = 1-\frac{6\sum d^2}{n(n^2-1)}
- Regression of y on x: y-\bar{y}=b_{yx}(x-\bar{x}), where b_{yx}=r\frac{\sigma_y}{\sigma_x}
- Laspeyres index: LPI=\frac{\sum p_1q_0}{\sum p_0q_0}\times 100
- Paasche index: PPI=\frac{\sum p_1q_1}{\sum p_0q_1}\times 100
- Fisher’s ideal index: F=\sqrt{LPI\times PPI}
Done — I turned it into a clean chart-style formula note you can add to your page. If you want, I can also make it into a table chart or a one-page printable PDF.
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Formula Chart: Time Value of Money, Series, and Statistics
| Topic | Formula |
|---|---|
| Simple Interest | SI = PRT |
| Compound Interest | A = P\left(1+\frac{R}{100}\right)^T |
| Effective Rate | ER = \left(1+\frac{R}{m}\right)^m - 1 |
| Future Value of Annuity | FV = A\left(\frac{(1+i)^n-1}{i}\right) |
| Present Value of Annuity | PV = A\left(\frac{1-(1+i)^{-n}}{i}\right) |
| Quadratic Roots | x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} |
| A.P. nth Term | a_n = a+(n-1)d |
| A.P. Sum | S_n=\frac{n}{2}[2a+(n-1)d] |
| G.P. nth Term | a_n = ar^{n-1} |
| G.P. Infinite Sum | (S_\infty=\frac{a}{1-r},\ |
| Mean | \bar{x}=\frac{\sum x}{n} |
| Empirical Relation | Mode=3(Median)-2(Mean) |
| Standard Deviation | \sigma=\sqrt{\frac{\sum (x-\bar{x})^2}{n}} |
| Coefficient of Variation | CV=\frac{\sigma}{\bar{x}}\times 100 |
| Karl Pearson Correlation | r=\frac{\sum (x-\bar{x})(y-\bar{y})}{\sqrt{\sum (x-\bar{x})^2\sum (y-\bar{y})^2}} |
| Spearman Rank Correlation | \rho=1-\frac{6\sum d^2}{n(n^2-1)} |
| Regression on x | y-\bar{y}=b_{yx}(x-\bar{x}) |
| Laspeyres Index | LPI=\frac{\sum p_1q_0}{\sum p_0q_0}\times 100 |
| Paasche Index | PPI=\frac{\sum p_1q_1}{\sum p_0q_1}\times 100 |
| Fisher’s Ideal Index | F=\sqrt{LPI\times PPI} |
Done. I formatted it as a chart-style table you can paste into your page.
If you want, I can also make:
- a color-coded revision chart, or
- a PDF one-pager for printing.
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