Paper 4: Fundamentals of Business Mathematics & Statistic

1.14 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Arithmetic

or, ( )^4

P^1000

1.025

=

∴ log P = log 1000 – 4log (1.025) = 3 – 4 (0.0107) = 3 – 0.0428 = 2.9572

∴ P = antilog 2.9572 = 906.1.

Hence the present amount = ` 906.10

[To find rate of interest]

Example 26 : A sum of money invested at C.I. payable yearly amounts to ` 10, 816 at the end of the second

year and to ` 11,248.64 at the end of the third year. Find the rate of interest and the sum.

Here A 1 = 10,816, n = 2, and A 2 = 11,248.64, n = 3

From A = P (1 + i)n we get,

10,816 = P (1 + i)^2 ... (i) and 11,248.64 = P(1 + i)^3 ... (ii)

Dividing (ii) by (i)

( )

( )

( )

3

2

11,248.64 P 1 i or, 1 i 11,248.64

10,816 P 1 i 10,816

= + + =

+

or i=11,248.6410,816 − =^1 10,816432.64=.04, r = i × 100 = .04 × 100 = 4 ∴ reqd. rate = 4%

Now from (I) ( )^2 ( )^2

P 10,816 10,816

1 .04 1.04

= =

+

Log P = log 10,816 – 2log (1.04) = 4.034 – 2 (0.170) = 4.034 – .0340 = 4.000

∴ P = antilog 4.000 = 10,000 ∴ required sum = ` 10,000.

SELF EXAMINATION QUESTIONS

1. The difference between the simple interest and compound interest on a sum put out for 2 years at 5%
   was 6.90. Find the sum. [Ans. 2,300]


2. Find the CI. on 6,950 for 3 years if the interest is payable half-yearly, the rate for the first two years being 6% p.a. and for the third year 9% p.a. [Ans. 1,589]


3. In what time will a sum of money double itself at 5% C.I. payable half-yearly? [Ans. 14.01 yrs.]


4. What is the rate per cent p.a. if 600 amount to 10,000 in 15 years, interest being compounded half-
   yearly. [Ans. 19.6%]


5. What is the present value of an investment of 2,000 due in 6 years with 5% interest compounded semi- annually? [Ans. 1,488]


6. A sum of 1000 is invested for 5 years at 12% interest per year. What is the simple interest? If the same amount had been invested for the same period at 10% compound interest per year, how much more interest would he get? [Ans. 162]


7. A certain sum is invested in a firm at 4% C.I. The interest for the second year is 25. Find interest for the 3 rd year. [Ans. 26]


8. The interest on a sum of money invested at compound interest is 66.55 for the second year and 72
   for the fourth year. Find the principal and rate per cent. [Ans. 1,600 ; 4%]