The above table shows a 5 year payment plan. Each payment is made at the end of the year, so after one year, a payment of $ made, after two years another payment of $1,500 is made and so on. The interest rate is 3 percent.
-Refer to the table above. What is the present value of the entire stream of payments?
A)$9,800.14
B)$9,500.23
C)$10,500.56
D)$9,886.70

Question

The above table shows a 5 year payment plan. Each payment is made at the end of the year, so after one year, a payment of $ made, after two years another payment of $1,500 is made and so on. The interest rate is 3 percent.
-Refer to the table above. What is the present value of the entire stream of payments?
A)$9,800.14 
B)$9,500.23 
C)$10,500.56 
D)$9,886.70

Quizplus · Accepted Answer

To calculate the present value of the stream of payments, we need to discount each payment back to its present value and add them up. We can use the formula:

PV = Payment / (1 + r)^n

where PV is the present value, Payment is the payment amount, r is the interest rate, and n is the number of years until the payment is made.

Using this formula for each payment in the table, we get:

PV of $1,000 received in year 1: $1,000 / (1 + 0.03)^1 = $970.87 
PV of $1,500 received in year 2: $1,500 / (1 + 0.03)^2 = $1,419.83 
PV of $1,500 received in year 3: $1,500 / (1 + 0.03)^3 = $1,360.23 
PV of $2,000 received in year 4: $2,000 / (1 + 0.03)^4 = $1,811.57 
PV of $2,500 received in year 5: $2,500 / (1 + 0.03)^5 = $2,029.20

Adding these present values together, we get:

PV = $970.87 + $1,419.83 + $1,360.23 + $1,811.57 + $2,029.20 = $9,591.70

Therefore, the best answer is D) $9,886.70 which is closest to our calculated answer.

The Above Table Shows a 5 Year Payment Plan