Question

Trish receives $550 on the first of each month. Josh receives $550 on the last day of each month. Both Trish and Josh will receive payments for next four years. At a discount rate of 9.5 percent, what is the difference in the present value of these two sets of payments?

	A.	$184.63
	B.	$198.61
	C.	$194.43
	D.	$188.59
	E.	$173.31

Answer 1

The difference is computed as shown below:

Present value if received at the end of month is computed as follows:

Present value = Monthly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

r is computed as follows:

= 9.5% / 12

= 0.791666667%

n is computed as follows:

= 4 x 12

= 48

So, the amount will be as follows:

= $ 550 x [ (1 - 1 / (1 + 0.00791666667)⁴⁸ ) / 0.00791666667 ]

= $ 21,892.17 Approximately

Now if we received the amount at the beginning, then we need to multiply the above amount by (1 + r) as shown below:

= $ 21,892.17 x (1 + 0.00791666667)

= $ 22,065.48 Approximately

So, the difference will be as follows:

= $ 22,065.48 - $ 21,892.17

= $ 173.31

So, the correct answer is option E.

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