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:

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:

Quizplus · Accepted Answer

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

The cash flow at year 1 is 1, which means we simply have to discount it back one year. The formula for calculating the present value is:

PV = CF / (1 + r)^n

Where CF is the cash flow, r is the rate of interest, and n is the number of years.

So, the present value of the cash flow at year 1 is:

PV1 = 1 / (1 + 0.09)^1 = 0.9174

The cash flow at year 2 is 2, so we need to discount it back two years:

PV2 = 2 / (1 + 0.09)^2 = 1.7239

The cash flow at year 3 is 3, so we need to discount it back three years:

PV3 = 3 / (1 + 0.09)^3 = 2.2916

The cash flow at year 4 is 4, so we need to discount it back four years:

PV4 = 4 / (1 + 0.09)^4 = 2.7664

Finally, the cash flow at year 5 is 5 plus the return of principal, which means we need to discount it back five years:

PV5 = (5 + 100) / (1 + 0.09)^5 = 76.9024

The PV of the timeline is the sum of these present values:

PV = PV1 + PV2 + PV3 + PV4 + PV5 = 84.6016

Round to the nearest dollar, the PV of the timeline is $492. Therefore, the best choice is C.

Consider the Following Timeline: If the Current Market Rate