Question

You recently got hired to work for Hank. You are set to receive an annual bonus of $12,900 per year for the next 16 years. Assume the interest rate is 7.8 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?

Answer 1

Present Value of the annual payment if they are received at the end of the year

Annual Payment (P) = $12,900

Interest Rate (r) = 7.80% per year

Number of years (n) = 16 Years

Therefore, the Present Value of an Ordinary Annuity = P x [{1 - (1 / (1 + r) n} / r]

= $12,900 x [{1 - (1 / (1 + 0.0780)¹⁶} / 0.0780]

= $12,900 x [{1 - (1 / 3.325831)} / 0.0780]

= $12,900 x [(1 - 0.300677) / 0.0780]

= $12,900 x [0.699323 / 0.0780]

= $12,900 x 8.965683

= $115,657.31

Present Value of the annual payment if they are received at the beginning of the year

Annual Payment (P) = $12,900

Interest Rate (r) = 7.80% per year

Number of years (n) = 16 Years

Therefore, the Present Value of an Annuity Due = (1 + r) x P x [{1 - (1 / (1 + r) n} / r]

= (1 + 0.0780) x $12,900 x [{1 - (1 / (1 + 0.0780)¹⁶} / 0.0780]

= 1.0780 x $12,900 x [{1 - (1 / 3.325831)} / 0.0780]

= 1.0780 x $12,900 x [(1 - 0.300677) / 0.0780]

= 1.0780 x $12,900 x [0.699323 / 0.0780]

= 1.0780 x $12,900 x 8.965683

= $124,678.58

Therefore, the amount of more payment will be $9,021.27 [$124,678.58 - $115,657.31]