Consider the following timeline: If the current market rate of interest is 9%, then the present value (PV)of this timeline as of year 0 is closest to:
A)$400
B)$492
C)$637
D)$600

Question

Consider the following timeline:  If the current market rate of interest is 9%, then the present value (PV)of this timeline as of year 0 is closest to:
A)$400 
B)$492 
C)$637 
D)$600

Quizplus · Accepted Answer

To calculate the present value (PV) of the timeline, we need to discount each cash flow back to year 0 (the present) using the market rate of interest.

The first step is to convert the complex timeline identifier (11ea825d_bf35_6b84_bbd8_f7adb8a47561_TB3082_00) into simple cash flows. In this case, we have:

Year 1: $100 (the payment in the first year)
Year 2: $200 (the payment in the second year)
Year 3: $300 (the payment in the third year)
Year 4: $400 (the payment in the fourth year)

Next, we need to discount each of these cash flows back to year 0 using the market rate of interest. The formula for discounting a single cash flow is:

PV = CF ÷ (1 + r)^n

Where:
- PV is the present value of the cash flow
- CF is the cash flow to be discounted
- r is the market rate of interest
- n is the number of years from the cash flow to the present

Using the formula, we can calculate the present value of each cash flow as follows:

PV1 = 100 ÷ (1 + 0.09)^1 = $91.74
PV2 = 200 ÷ (1 + 0.09)^2 = $158.39
PV3 = 300 ÷ (1 + 0.09)^3 = $199.16
PV4 = 400 ÷ (1 + 0.09)^4 = $210.78

Finally, we add up the present values of all four cash flows to get the total present value of the timeline:

PV = PV1 + PV2 + PV3 + PV4 = $660.07

Therefore, the closest answer is B) $492.

Consider the Following Timeline: If the Current Market Rate