Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 1.17

Example 29 :
The accumulation in a Providend Fund are invested at the end of every year to year 11% p.a. A person
contributed 15% of his salary to which his employer adds 10% every month. Find how much the
accumulations will amount to at the end of 30 years for every 100 rupees of his monthly salary.

Solution:
Let the monthly salary of the person be Q, then the total monthly contribution to provident fund = 0.15Q+ 0.1Q= 0.25Q Total annual contributions to provident fund =(0.25Q x 12) = `3Q.
If A be the total accumulation at the end of 30 year.

Then A = Pi{(1 i 1+)n−} Here P = 3Q, i= 10011 =0.11, n = 30

∴A=0.113Q{(1 0.11) 1+^30 −}=0.113Q(22.89 1−)

A^3 Q 21.89 597Q

∴ =0.11× =

So for each 100 of the person’s salary, the accumulation =(597×100) [{Q = 100]
= `59,700.
Let x = (1.11)^30
∴ logx = log (1.11)^30
= 30 × log 1.11
= 30 × .0453
= 1.359
x = Antilog 1.359
= 22.89

Example 30 :
A loan of 10,000 is to be repaid in 30 equal annual instalments ofP. Find P if the compound interest
charged is at the rate of 4% p.a.
Given (1.04)^30 = 3.2434.
Solution:

Present Value = V = Pi{1 1 i−(+)−n} Here V = `10,000

10,000 = 0.04P {1 1 0.04− +( )−^30 } i = 1004 = 04.0

or, 10,000 = 0.04P {1 1.04−( )−^30 } n = 30

or, 10,000x 0.04 =

P 1^1

3.2434

(^) −
or, 400 = P×2.24343.2434
or, P = 400 3.24342.2434× = `578.30.