Manipulation of a summation with application to finance math and interest rates.
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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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Solution Summary
A proof that relates annuity-certain to interest rate is performed.
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By definition
a_n = v + v^2 + .... + v^n (1)
and so multiplying both sides of (1) by v gives
va_n = v^2 + v^3 + .... + v^{n+1}. ...
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