Question

Foster owns a small business and has received an interesting offer from Sapphire Bank. The bank has offered to pay him a new customer incentive of $138 at the end of each year, with the amount increasing by 4% each subsequent year, as long as he continues to use the bank for all of his business needs. The bank will make the payments to him for 6 years. In addition, the bank will pay him a bonus of $217 at the end of year 2.

His current bank is trying to retain his business by offering to immediately give him a toaster and season tickets to the local sports team if he commits to staying with the bank for 5 more years.

Foster is trying to compare the two offers in terms of monetary value. Calculate the present value of the payments and the bonus from Sapphire Bank using an interest rate of 4% compounded annually. (In other words, how much are all of the payments worth today?)

Note: Foster would receive the first payment from Sapphire Bank at the end of year 1.

Answer 1

The present value of the series = C*n/(1+i)

C = 138

n = 6

i = 4% = 0.04

PV = 138*6/(1+0.04) = 828/1.04 = 796.15

PV of the bonus = 217*(P/F,4%,2) = 217*0.924556 = 200.628

Total = 796.15+200.628 = 996.78 = 997