Paper 4: Fundamentals of Business Mathematics & Statistic

1.20 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Arithmetic

SOLVED EXAMPLES :

(T.D; n; i are given, to find A)

Example 33 : The true discount on a bill due 6 months hence at 8% p.a. is ` 40, find the amount of the bill.

In the formula, T.D=1 niAni+ , T.D. = 40, n=12 26 1= , i = 8/100 = 0.08

A. .(0.08)^1

40 2

1 (0.08)^1

2

∴ =

+ , or, A = 1040 (in `)

Example 34 : (T.D.; A, i are given, to find n)

Find the time when the amount will be due if the discount on ` 1,060 be ` 60 at 6% p.a.

T.D. Ani,or,60 1060.n.(0.06)

=1 ni+ = 1 n(0.06)+ or,

n^2

= 3 yrs.

Example 35 : (T.D.; A; n are given, to find i)

If the discount on ` 11,000 due 15 months hence is ` 1,000, find the rate of interest,

Here, A =11,000, n=15 512 4= , T.D. =1000, i =?

So we have,

11000 5 i

1000 4 or,

1 5 i

4

× ×

=

+ ×

12500 i = 1000 or i = 0.08.

Example 36 : (If A, n; i; are given to find T.D.)

Find the T.D. on a sum of ` 1750 due in 18 months and 6% p.a.

HereA 1750;n^18 yrs. .yrs; i^36 0.06

= = 17 = 2 = 100 =

So we get

1750 3 0.06

T.D.^2 1750 0.09 144.50 (approx)

1 3 0.06 1 0.09

2

× × ×

= = + =

+ ×

`

∴reqd. T. D. 144.50.=`

Example 37 : Find the present value of ` 1800 due in 73 days hence at 7.5% p.a. (take 1 year = 365 days)

Here : A = 1800, n=365 573 1= years; i= 1007 .5=0.075

1 800. .(0.075)^1

T.D.^5 1800 0.015 27 26.60

1 (0.075)^1 1 0.015 1.015

5

= = × = =

+ + `

We know P.V. = A – T.D. ∴ P.V. = 1800 – 26.60 = 1773.40