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 lowest annual interest rate at which you would prefer the lump-sum payment over the four annual payments?
A)2%
B)5%
C)7%
D)10%

Question

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 lowest annual interest rate at which you would prefer the lump-sum payment over the four annual payments?
A)2%
B)​5%
C)​7%
D)​10%

Quizplus · Accepted Answer

To compare the two options, we can calculate the present value of the four annual payments using the formula:
present value = annual payment / (1 + interest rate)^n
Where n is the number of years until each payment is received.
Using a financial calculator or spreadsheet, we can find that the present value of the four annual payments is $9,848.69 at a 5% annual interest rate.
Therefore, if the annual interest rate is less than 5%, we would prefer the lump-sum payment of $10,000. If the annual interest rate is greater than 5%, we would prefer the four annual payments of $2,750. 
Option B with an annual interest rate of 5% is the threshold rate at which the present value of the four annual payments equals the lump-sum payment, so any annual interest rate below 5% would make the lump-sum payment preferable.

Suppose You Have a Choice Between Receiving a Lump-Sum Payment