PYQ Vault

CDS Mathematics · Formula sheet

Simple and Compound Interest formulas

5 formulas and 5 common traps for CDS Mathematics Simple and Compound Interest, grouped by subtopic.

Full notes with worked examples

Simple Interest

Learn this subtopic in the notes

SI = PRT/100

Simple interest

SI=PRT100\text{SI} = \dfrac{PRT}{100}

Common traps

Triples means twice the sum in interest

A sum that triples has earned 2P2P, not 3P3P. The amount includes the principal; the interest does not.

Compound Interest

Learn this subtopic in the notes

The amount formula and compounding periods

Compound amount

A=P(1+r100)nA = P\left(1 + \dfrac{r}{100}\right)^n

Doubling times and growth factors

Growth condition

(1+r100)n>k\left(1 + \dfrac{r}{100}\right)^n > k

Common traps

Adjust both the rate and the periods

Quarterly compounding at 12%12\% is 3%3\% for FOUR periods a year. Using 12%12\% with four periods, or 3%3\% for one, gives a wrong amount.

Four times is two doublings, not four

A sum that doubles in 55 years is four times itself after 1010, not 2020. Compound growth multiplies; it does not add.

CI Minus SI, and Instalments

Learn this subtopic in the notes

The gap between CI and SI

Two-year gap

CI−SI=P(r100)2\text{CI} - \text{SI} = P\left(\dfrac{r}{100}\right)^2

Equal instalments

Two instalments

X1+r+X(1+r)2=P\dfrac{X}{1 + r} + \dfrac{X}{(1 + r)^2} = P

Common traps

The two-year formula is for two years only

For three years the gap is P(r/100)2(3+r/100)P(r/100)^2(3 + r/100), not P(r/100)3P(r/100)^3 and not P(r/100)2P(r/100)^2. Use the formula for the years asked, or compute both interests.

Discount each payment separately

The second instalment is discounted over TWO years, not one. Dividing the loan in half and adding a year's interest gives an option that is always offered and always wrong.

More CDS Mathematics formula sheets