Consider the following timeline:

If the current market rate of interest is 8%, 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 8%, then the present value (PV) of this timeline as of year 0 is closest to ________.

BlackTom AI · Accepted Answer

Discount each future cash flow to time 0 using the formula PV = CFt / (1 + r)^t. Relevant concepts: time value of money, present value of single future cash flows, and discounting at the market rate (8%).

Step-by-step calculation:
1) Year 1 cash flow: $100 discounted one year at 8%
   PV1 = 100 / (1.08) = 100 / 1.08 = 92.5925926
2) Year 2 cash flow: $200 discounted two years at 8%
   1.08^2 = 1.1664
   PV2 = 200 / 1.1664 = 171.4677641
3) Year 3 cash flow: $300 discounted three years at 8%
   1.08^3 = 1.259712
   PV3 = 300 / 1.259712 = 238.1149880

Add the discounted amounts:
PVtotal = PV1 + PV2 + PV3
PVtotal = 92.5925926 + 171.4677641 + 238.1149880 = 502.1753447

Rounding to the nearest dollar gives $502, which is the present value at year 0.

Why this is correct: each cash flow is worth less today than its future nominal amount because money could earn 8% per year. By discounting each payment back to time 0 and summing, we get the total value today. The calculated sum (about $502.18) matches the provided correct choice $502.

Why the other options are incorrect:
- $1,004 would equal approximately twice the correct PV (not justified by any doubling in the timeline).
- $600 and $653 are higher than the properly discounted sum; they correspond to under-discounting or misplacing cash flows (for example, treating later cash as if it were earlier or using a lower discount rate).

Conclusion: The present value as of year 0 is approximately $502, matching the given correct answer.

Consider the following timeline: If the current market rate of interest is 8%, then the present value (PV) of this timeline as of year 0 is closest to ________.单项选择题

类似问题

Sara wants to have $600,000 in her savings account when she retires. How much must she put in the account now, if the account pays a fixed interest rate of 8%, to ensure that she has $600,000 in 20 years?

Which one of the following will produce the lowest present value interest factor?

What is the value today of $1,500 per year, at a discount rate of 10 percent, if the first payment is received 5 years from now and the last payment is received 23 years from today?

Salvatore has the opportunity to invest in a scheme which will pay $5000 at the end of each of the next 5 years. He must invest $10,000 at the start of the first year and an additional $10,000 at the end of the first year. What is the present value of this investment if the interest rate is 3%?

You are promised $5,000 at a fixed positive interest rate. Compare two scenarios: (1) You receive $5,000 in 3 years, and (2) You receive $5,000 in 8 years. Which statement must be true?[Fill in the blank]

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单