Question

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

Answer 1

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)¹⁵ ) / 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)¹⁵ ) / 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

Feel free to ask in case of any query relating to this question