Question

What single amount on April 1, 2012, is equivalent to a series of equal, semiannual cash flows of $5200 that starts with a cash flow on January 1, 2010, and ends with a cash flow on January 1, 2019? The interest rate is 6% and compounding is quarterly?

Answer 1

The single amount on April 1, 2012 that is equivalent to a series of equal, semiannual cash flows of $5200 is; $57,023.2

Compound Interest Factor

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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