342 MATHEMATICS
Step 3 (Solving the problem) : From (1) and (2)
1790 1
100 12 r
=20
or r =
20 1200
1790
✁
= 13.14 (approx.)Step 4 (Interpreting the solution) : The rate of interest charged in the instalment
scheme = 13.14 %.
The rate of interest charged by the bank = 10%
So, she should prefer to borrow the money from the bank to buy the bicycle which is
more economical.
Step 5 (Validating the model) : This stage in this case is not of much importance
here as the numbers are fixed. However, if the formalities for taking loan from the
bank such as cost of stamp paper, etc., which make the effective interest rate more
than what it is the instalment scheme, then she may change her opinion.
Remark : Interest rate modelling is still at its early stages and validation is still a
problem of financial markets. In case, different interest rates are incorporated in fixing
instalments, validation becomes an important problem.
EXERCISE A2.2
In each of the problems below, show the different stages of mathematical modelling for solving
the problems.
- An ornithologist wants to estimate the number of parrots in a large field. She uses a net
to catch some, and catches 32 parrots, which she rings and sets free. The following
week she manages to net 40 parrots, of which 8 are ringed.
(i) What fraction of her second catch is
ringed?
(ii) Find an estimate of the total number
of parrots in the field. - Suppose the adjoining figure represents
an aerial photograph of a forest with each
dot representing a tree. Your purpose is to
find the number of trees there are on this
tract of land as part of an environmental
census.