Question 148058
The future value of money using compound interest is given by:

{{{F = P(1+(r/n))^(nt)}}}
Where
F is the future value
P is the present value
r s the annual interest rate
n is the number of compounding per year
t is the total number of compoundings

This problem asks for the present value (P)of a future sum (F=5000), when the interest is 8%(r=0.08) compounded semi-annually (n=2) for a length of 8 years (t = 8*n = 16). 

Solving for P:
{{{F = P(1+(r/n))^(nt)}}}
{{{5000 = P(1+(0.08/2))^(2*8)}}}
{{{5000 = P(1+(0.04))^(16)}}}
{{{5000 = P(1.04)^(16)}}}
{{{5000/((1.04)^(16)) = P}}}
{{{5000/1.872 = P }}}
{{{2669.54 ~=P}}}

The answer is C

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