FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 1.19- A loan of
5,000 is to be paid in 6 equal annual payments, interest being at 8% per annum compound interest and the first payment be made after a year. Analyse the payments into those on account of interest and an account of amortisation of the principal. [Ans.1,081.67] - Mrs. S. Roy retires at the age of 60 and earns a pension of
60,000 a year. He wants to commute on- fourth of his pension to ready money. If the expectation of life at this age be 15 years, find the amount he will receive when money is worth 9% per annum compound. (It is assumed that pension for a year is due at the end of the year). [Ans.1,20,910.55] - A Government constructed housing flat costs `1,36,000; 40% is to be paid at the time of possession
and the balance reckoning compound interest @9% p.a. is to be paid in 12 equal annual instalments.
Find the amount of each such instalment. [Given )09.1( 12
1
= 0.35587]
- Find the present value of an annuity of
300 p.a. for 5 years at 4%. Given log 104 = 2.0170333, log 0.0821923 = 9148335.2. [Ans.1,335.58] - A person purchases a house worth
70,000 on a hire purchase scheme. At the time of gaining possession he has to pay 40% of the cost of the house and the rest amount is to be paid in 20 equal annual instalments. If the compound interest is reckoned at 721 % p.a. What should be the value of each instalment? [Ans.4,120]
1.3 DISCOUNTING OF BILLS AND AVERAGE DUE DATE
Few Definitions :
Present Value (P.V.) : Present value of a given sum due at the end of a given period is that sum which
together with its interest of the given period equals to the given sum i.e.
P.V. + Int. on P.V. = sum due [Sum due is also known as Bill Value (B.V.)]
Symbols : If A = Sum due at the end of n years, P = Present value, i = int. of ` 1 for 1 yr.
n= unexpired period in years, then A = P+P n i = P(1+n i).......(i)
or, P=1 ni+A
True Discount (T.D) :
True discount of a given sum due at the end of a given period, is the interest on the present value of the
given sum i.e. T.D. = P n i..............(ii)
T.D.= Int. of P.V. = amount due – Present value i.e. T.D. = A – P.........(iii)
Again T.D. = A−1 ni 1 ni+A = Ani+ ............(iv)
i.e. Find P.V. and T.D. of ` 327 due in 18 months hence at 6% S.I..
327 3 6
T.D Ani 2 100 27,
1 ni 1 3 6
2 100× ×
= + = =
+ × here A = 327, n = 18 m = 3/2 yrs. i= 6/100.We know P.V. +Int. on PV (i.e.T.D)= sum due (i.e.B.V)
Or, P.V. = B.V.– T.D. = 327 – 27 = ` 300.