The single amount on April 1, 2012 that is equivalent to a series of equal, semiannual cash flows of $5200 is; $57,023.2
<h3>Compound Interest Factor</h3>
We are given;
Semi annual cash Flow; A_sa = $5200
Interest rate; r = 6%
From April 1, 2012 to January 1 2019 is 6.75 years
Thus; Period; T = 6.75 years
Cash flows is semi annual. Thus; t_a = 1/2
Thus; n_sa = 6.75 * 2
n_sa = 13.5
i_sa = 6% * 1/4 = 1.5%
Thus;
Single amount = 5200 * (P/A, 1.5%, 13.5)
From compound interest tables, P/A at n = 13.5 and at i = 3% by interpolation gives 10.966. Thus;
Single amount = 5200 * 12.137
Single amount = $63,112.4
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