Paper 4: Fundamentals of Business Mathematics & Statistic

1.18 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Arithmetic

Example 31 :

A Professor retires at the age 60 years. He will get the pension of `42,000 a year paid in half-yearly instalment

of rest of his life. Reckoning his expectation of life to be 15 years and that interest is at 10% p.a. payable half-

yearly. What single sum is equivalent to his pension?

Solution:

The amount of pension = `42,000

∴ P = `42,000; n = 15 = number of years

i = 10% payable half-yearly = .10

We have,

V = ( )

30

P 1 1 i)2n 42,000 1 1 0.10

i 0.10 2

−

(^) − + − (^) =^ −^ +^
(^)
= 4,20,000[1– (1.05)–30] = 4,20,000 (1– 0.23138)
= 4,20,000x 0.76862 = 3,22,820.40
Hence, 3,22,820.40 is the amount of single sum equivalent to his pension. Example 32 : A man purchased a house valued at3,00,000. He paid 2,00,000 at the time of purchase and agreed to pay the balance with interest of 12% per annum compounded half yearly in 20 equal half yearly instalments. If the first instalment is paid after six months from the date of purchase, find the amount of each instalment. [Given log 10.6 = 1.0253 and log 31.19 = 1.494] Solution: Since2,00,000 has been paid at the time of purchase when cost of house was 3,00,000, we have to consider 20 equated half yearly annuity paymentP when 12% is rate of annual interest compounded half
yearly for present value of 1,00,000. ∴ 1,00,000 = 12.0P2 [1– (1+ .06)–20] or, 1,00,000× 0.12 = 2P [1– (1.06)–20] or, 12,00,000 = 2P [1– .3119] or, 6,00,000 = Px .6881 ∴ P =. 6881 000,00,6 =8,718.40.
∴ Amount of each instalment = `8,718.40.
Let x = (1.06)–20
∴ logx = –20 log 1.06 = – 20 x .0253
= –0.506 = T.496 = log.3119
∴ x = 0.3119
Self Examination Questions

1. Mr. S Roy borrows 20,000 at 4% compound interest and agrees to pay both the principal and the interest in 10 equal annual instalments at the end of each year. Find the amount of these instalments. [Ans.2,466.50]


2. A man borrows 1,000 on the understanding that it is to be paid back in 4 equal instalments at intervals of six months, the first payment to be made six months after the money was borrowed. Calculate the value of each instalment, if the money is worth 5% p.a. [Ans.266]


3. A persons invests 1,000 every year with a company which pays interest at 10% p.a. He allows his deposits to accumulate with the company at compound rate. Find the amount standing to his credit one year after he has made his yearly investment for the tenth time? [Ans.17,534]