FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 1.15- Determine the time period during which a sum of
1,234 amounts to5,678 at 8% p.a. compound
interest, payable quarterly. (given log 1234 = 3.0913, log 5678 = 3.7542 and log 1.02 = 0.0086]
[Ans. 19.3 yrs. (approx)]
[hints : 5678 = 1234
0.08 4n(^1) + 4 & etc.]
- Determine the time period by which a sum of money would be three times of itself at 8% p. a. C.I.
(given log 3= 0.4771, log 10 1.08 = 0.0334) [Ans. 14.3 yrs. (approx)] - The wear and tear of a machine is taken each year to be one-tenth of the value at the beginning of
the year for the first ten years and one-fifteenth each year for the next five years. Find its scrap value
after 15 years. [Ans. 24.66%] - A machine depreciates at the rate of 10% p.a. of its value at the beginning of a year. The machine was
purchased for44,000 and the scrap value realised when sold was25981.56. Find the number of years
the machine was used. [Ans. 5 years (approx)]
1.2.3 ANNUITIES
Definition:
An annuity is a fixed sum paid at regular intervals under certain conditions. The interval may be either a year
or a half-year or, a quarter year or a month.
Definition: Amount of an annuity:
Amount of an annuity is the total of all the instalments left unpaid together with the compound interest of
each payment for the period it remains unpaid.
Formula:
(i) A = Pi{(1 i) 1+ n−} Where A = total(s) amount after n years,
i = rate of interest per rupee per annum.
p =yearly annuity
(ii) If an annuity is payable half-yearly and interest is also compounded half-yearly, then amount A is given
by
A =2P i^2 n
i^121(^)
- −
(^)
(iii) If an annuity is payable quarterly and interest is also compounded quarterly, then amount A is given by
A =
4P i 4n
i^141
(^) - −
(^)
Present value of an annuity:
Definition: Present value of an annuity is the sum of the present values of all payments (or instalments)
made at successive annuity periods.