Manipulation of a summation with application to finance math and interest rates.
Please see the attached file for the fully formatted problem.
In financial mathematics, when valuing cash flows, an important function is the so-called immediate annuity-certain, a_n, which is defined by the relation
a_n = v + v^2 + v^3 + ....... + v^n
where v:=(1+i)^(-1) and i represents the effective rate of interest per annum. Prove that
a_n = (1-v^n)/i
If the effective rate of interest is 3% pa, find a_4 to 3 decimal places.
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