Quant (Concepts): SI & CI (part-1)

Quant (Concepts): SI & CI (part-1)

Quick Review: Simple Interest and Compound Interest

Simple Interest = (P × R × T)/100, where, P is the amount invested or borrowed, T is the time in years and R is the annual interest rate.

A = P + SI, where, A is the amount payable or receivable at the end of period T, P is the principal and SI is the simple interest.

A = P(1+R/100)ⁿ, where, A is the amount receivable on compound interest basis, P is the principal invested, R is the annual rate of interest and n is the number of years for which the sum has been invested.

Compound Interest = A - P, where, C.I is the compound interest, A is the amount receivable with interest and P is the principal invested.

Interest rate on monthly installment plans:

R = 24×I×100/N(F+L), where, R is the interest, I is the installment, N is the number of installments, F is the principal left before the first installment and L is the principal left before last installment.

Equated Installment

X is the equated installment, A is the amount borrowed, R is the rate of interest and n is the number of years.

• A = P(1+R/200)^2N, if the interest is calculated half-yearly.
• A = P(1+R/400)^4N, if the interest is calculated quarterly.

Rule of 72 - Time taken to double one’s investment can be obtained by dividing 72 by the interest rate. This is only in case of compound interest.

Rule of 69 - This rule is also used to determine the time taken to double one’s investment. However, it is a more refined formula. Time taken = 0.35 + (69/Interest rate). This is also true in case of compound interest only.

• If D is the difference in CI and SI for 2 years, and R is the rate of interest and P the principal then, D=R/100×R/100×P
• The following table lists the values of an initial investment, P = Re. 1 for certain time periods and rates of interest, calculated at both, simple and compound interest. This would be of great help in time management during the paper, if memorized.

Time ⇓ Rate ⇒	5%		10%		20%		30%
	S.I	C.I	S.I	C.I	S.I	C.I	S.I	C.I
1 year	1.05	1.05	1.1	1.1	1.2	1.2	1.3	1.3
2 yrs	1.10	1.1025	1.2	1.21	1.4	1.44	1.6	1.69
3 yrs	1.15	1.1575	1.3	1.331	1.6	1.728	1.9	2.197
4 yrs			1.4	1.4641	1.8	2.0736