A principal £P is invested at r% interest for 1 year.
a) Find the formula of the future value in terms of P and u, where $u = \frac{r}{100}$ if the interest is compounded:
i. semi-annually
ii. monthly
iii. weekly
In each of the three cases, you need to state the equivalent annual rate and the rate for each compound
period in terms of u.
b) Use the results in part a) to derive the formula when the interest is compounded continuously. You
need to explain, in your own words, the method used.
Mr Cook has £13 500 to invest. He is considering two possible investments:-
Investment A: at (N+2)% interest compounded annually for N years;
Investment B: at (N+1)% interest compounded continuously.
In both investments, N is the same natural number.
c) Investigate and explain which investment you would recommend depending on the number of years,
N.
Note:
For part a) i. for example you need to state the rate in the first 6 months and the rate in the last 6 months
in terms of u.
For part b) you need to research the following limit
$\lim_{x \to \infty} (1 + \frac{a}{x})^x$, where a is a non- zero real number
For part c) you may want to use Excel to support you with the calculations, but you need to state all the
formulae used.
