Question

Trish receives $450 on the first of each month. Josh receives $450 on the last day of each month. Both Trish and Josh will receive payments for next four years. At a discount rate of 9.5 percent, what is the difference in the present value of these two sets of payments?
-$162.50
-$159.08
-$154.30
-$151.06
-$141.80

Answer 1

Answer:

The last option is the answer -$141.80

Explanation:

we will use the present value formula for Trish she gets paid every first day of the month therefore she will receive an immediate payment of cash flow which will be added to the present value of future periodic value. Therefore we will find the difference between present values for Trish and Josh which have the same amounts which they'll receive per month.

Given: Trish and josh both receive $450 per month therefore that will be C the monthly future payment that will be received.

They will receive these amounts in a course period of Four years so that will be n = 4 x12=48  because we know that they will receive these payments every month or on a monthly basis for four years. which n represent periodic payments.

i which is the discount rate of 9.5%/12 as we know they will recieve these amounts monthly.

Therefore using the following formulas for present value annuity:

Pv = C[(1-(1+i)^-n)/i] and Pv= C[(1-(1+i)^-n)/i](1+i) then get the difference between these two present values for Trish and Josh.

therefore we will substitute the above values on the above mentioned formula to get the difference:

Pv= 450[(1-(1+9.5%/12)^-48)/(9.5%/12)]  - 450[(1-(1+9.5%/12)^-48)/(9.5%/12)](1+9.5%/12)    then we compute and get

Pv= $17911.77614 - $18053.5777

Pv = -$141.80 is the difference between the two sets of present values as one has an immediate payment and one doesn't have it.