Paper 4: Fundamentals of Business Mathematics & Statistic

1.12 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Arithmetic

FEW FORMULAE :

Compound Interest may be paid half-yearly, quarterly, monthly instead of a year. In these cases difference

in formulae are shown below :

(Taken P = principal, A = amount, T = total interest, i = interest on Re. 1 for 1 year, n = number of years.)

Time Amount I = A – P

(i) Annual A= P(1 + I)n I = P {(1 + i)n –1}

(ii) Half-Yearly

i 2n

A P 1=^ + 2

i^2 n

I P 1 2 1

(^)
= + −
(^)
(iii) Quarterly
i 4n
A P 1=^ + 4
i 4n
I P 1 4 1
(^)
= + −
(^)
In general if C.I. is paid p times in a year, then
i pn
A P 1=^ +p.
i.e. : Let P = ` 1000, r = 5% i.e., i = 0.05, n = 24 yrs.
If interest is payable yearly the A = 1000 (1 + 0.5)^24
If int. is payable half-yearly the A =

0.05 2 24

1000 1 2

×

• (^)
  If int. is payable quarterly then A =

0.05 4 24

1000 1 4

×

• (^)
  Note. or r = 100 I = interest per hundred.
  If r = 6% then If, however i = 0.02 then, r = 100 × 0.02 = 2%.
  SOLVED EXAMPLES. (using log tables)
  [To find C.I.]
  Example 22 : Find the compound interest on 1,000 for 4 years at 5% p.a. Here P = 1000, n = 4, i = 0.05, A =?
  We have A = P (1 + i)n
  A = 1000 (1+ 0.05)^4
  Or log A = log 1000 + 4log (1 + 0.05) = 3 + 4 log (1. 05) = 3 + 4 (0.0212) = 3 + 0.0848 = 3.0848
  A = antilog 3.0848 = 1215
  C.I. = 1215 – 1000 = ` 215
  [To find time]
  Example 23 : In what time will a sum of money double itself at 5% p.a. C.I.
  Here, P = P, A = 2P, i = 0.05, n =?