Question

Will must make quarterly estimated income tax payments to the Internal Revenue Service. The amounts and timing of these payments are shown below. Also shown are the monthly interest rates that apply to each interval of time. What is the P-equivalent of Will's payments on January 15? Jan. 15 April 15 June 15 Sept. 15 mo. mo. mo. $9,000 $11,000 $12,000 $9,000 The P-equivalent of Will's payments on January 15 is $ 40913. (Round to the nearest dollar.)

40913 is incorrect. find answer using this formula.

Answer 1

As is directed first discount the cash glow of September for 3 months at a rate of (3/4)% per month

$\large P_{June} = 12,000 + \frac{9,000}{(1+0.0075)^3}$

$\large P_{June} = 12,000 + 8,800.49$

$\large P_{June} = 20,800.49$

Now calculate the present value of April

$\large P_{April} =11,000 + \frac{ 20,800.49}{(1+.005)^3}$

$\large P_{April} =31,491.58$

Present Value of January

$\large P_{January} =9000 + \frac{31,491.58}{(1+0.0025)^3}$

$\large P_{January } =9000 + 31,256.56$

$\large P_{January} =\$ 40,256.56$

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