Question

Please explain how to do this by hand (w/o a financial calculator): Suppose you have a choice between receiving a lump-sum payment of $10,000 today or four annual payments of $2,750 (with the first payment one year from today). Of the following, which is the highest annual interest rate at which you would prefer the four annual payments over the lump-sum payment?

2%

5%

7%

10%

Answer 1

As per the question a choice has to be made in receiving $10,000 today or four annual payments of $2,750

Present worth (PW) of four annual cash flows when interest rate i=2%

PW=2750(P/A,2%,4) = 2750(3.8077) =$10,471.175 (highest)

Present worth (PW) of four annual cash flows when interest rate i=5%

PW=2750(P/A,5%,4) = 2750(3.5460) =$9751.5

Present worth (PW) of four annual cash flows when interest rate i=7%

PW=2750(P/A,7%,4) = 2750(3.3872) =$9314.8

Present worth (PW) of four annual cash flows when interest rate i=10%

PW=2750(P/A,10%,4) = 2750(3.1699) =$8717.225

Among the four annual interest rate, annual interest rate =2% is preferred for annual payments   over lump-sum payments because, the present worth of the annual cashflow is highest at this annual interest rate and it is more than the lump sum payment of $10,000.