Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 1.

Example 20 : In a certain time 1200 becomes 1560 at 10% p.a. simple interest. Find the principal that
will become ` 2232 at 8% p.a. in the same time.
In 1st case : P = 1200, A = 1560, i = 0.10, n =?
1560 = 1200 [1+n (.10)] = 1200 + 120 n
or, 120 n = 360 or, n = 3
In 2nd case : A = 2232, n = 3, i = 0.08, P =?
2232 = P (1+3×0.08) = P (1 + 0.24) = 1.24 P

or, P=^22 1.24^32 =1800.

Example 21 : A person borrowed 8,000 at a certain rate of interest for 2 years and then 10,000 at 1%
lower than the first. In all he paid ` 2500 as interest in 3 years. Find the two rates at which he borrowed the
amount.
Let the rate of interest = r, so that in the 2nd case, rate of interest will be (r–1). Now

8000 r 2 10,000 (r 1) 1 2500

100 100

× × + × − × =

or, 160r + 100 r – 100 = 2500 or, r = 10
In 1st case rate of interest = 10% and in 2nd case rate of interest = (10 – 1) = 9%
Calculations of interest on deposits in a bank : Banks allow interest at a fixed rate on deposits from a fixed
day of each month up to last day of the month. Again interest may also be calculated by days.

SELF EXAMINATION QUESTIONS

1. What sum will amount to 5,200 in 6 years at the same rate of simple interest at which 1,706 amount to 3,412 in 20 years? [Ans. 4000]


2. The simple interest on a sum of money at the end of 8 years is^25 th of the sum itself. Find the rate
   percent p.a. [Ans. 5%]


3. A sum of money becomes double in 20 years at simple interest. In how many years will it be triple?
   [Ans. 40 yrs.]


4. At what simple interest rate percent per annum a sum of money will be double of it self in 25 years?
   [Ans. 4%]


5. A certain sum of money at simple interest amounts to 560 in 3 years and to 600 in 5 years. Find the
   principal and the rate of interest. [Ans. ` 500; 4%]


6. A tradesman marks his goods with two prices, one for ready money and the other for 6 month’s credit.
   What ratio should two prices bear to each other, allowing 5% simple interest. [Ans. 40 : 41]


7. A man lends ` 1800 to two persons at the rate of 4% and^421 % simple interest p.a. respectively. At the

end of 6 years, he receives ` 462 from them. How much did he lend to each other?

[Ans. ` 800; ` 1000]