Question

You are set to receive an annual payment of $11,800 per year for the next 14 years. Assume the interest rate is 6.7 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?

a. $6820.28

b. $6600.28

c. $6270.26

d. $7392.31

e. $7040.29

Answer 1

Present value is computed as shown below:

= Future value / (1 + r)ⁿ

Present value if payments are at beginning of year is computed as follows:

= $ 11,800 + $ 11,800 / 1.067¹ + $ 11,800 / 1.067² + $ 11,800 / 1.067³ + $ 11,800 / 1.067⁴ + $ 11,800 / 1.067⁵ + $ 11,800 / 1.067⁶ + $ 11,800 / 1.067⁷ + $ 11,800 / 1.067⁸ + $ 11,800 / 1.067⁹ + $ 11,800 / 1.067¹⁰ + $ 11,800 / 1.067¹¹ + $ 11,800 / 1.067¹² + $ 11,800 / 1.067¹³

= $ 112,119.3076

Present value if payments are at end of year is computed as follows:

= $ 11,800 / 1.067¹ + $ 11,800 / 1.067² + $ 11,800 / 1.067³ + $ 11,800 / 1.067⁴ + $ 11,800 / 1.067⁵ + $ 11,800 / 1.067⁶ + $ 11,800 / 1.067⁷ + $ 11,800 / 1.067⁸ + $ 11,800 / 1.067⁹ + $ 11,800 / 1.067¹⁰ + $ 11,800 / 1.067¹¹ + $ 11,800 / 1.067¹² + $ 11,800 / 1.067¹³ + $ 11,800 / 1.067¹⁴

= $ 105,079.0137

So the difference is as follows:

= $ 112,119.3076 - $ 105,079.0137

= $ 7,040.29 Approximately

So, the correct answer is option e.

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