You are set to receive an annual payment of $11,900 per year for the next 15 years. Assume the interest rate is 6.8 percent. How much more are the payments worth if they are received at the beginning of the year rather than the end of the year?
Multiple Choice
$7,230.88
$6,647.75
$7,837.34
$7,464.14
$6,997.63
Present value if payments are at beginning of year is computed as shown below:
Present value = Annual payment x [ (1 – 1 / (1 + r)^{n}) / r ]
= $ 11,900 x [ (1 - 1 / (1 + 0.068)^{1}^{5} ) / 0.068 ]
= $ 11,900 x 9.224093582
= $ 109,766.7136
Since the payments are at the beginning, hence we need to multiply the above figure by (1 + r) as shown:
= $ 109,766.7136 x 1.068
= $ 117,230.8502
Present value if payments are at end of year is computed as shown below:
Present value = Annual payment x [ (1 – 1 / (1 + r)^{n}) / r ]
= $ 11,900 x [ (1 - 1 / (1 + 0.068)^{1}^{5} ) / 0.068 ]
= $ 11,900 x 9.224093582
= $ 109,766.7136
So, the difference will be as follows:
= $ 117,230.8502 - $ 109,766.7136
= $ 7,464.14 Approximately
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