An investor who was not as astute as he believed invested $281,000 into an account 6 years ago. Today, that account is worth $217,200. What was the annual rate of return on this account?

Question

BlackTom AI · Accepted Answer

We begin by identifying the key values and the time period: an initial investment (present value) of 281,000 is grown to a final value of 217,200 over 6 years. The problem asks for the annual rate of return, r, assuming compounding annually, so the formula is FV = PV × (1 + r)^t.

Option-by-option analysis:
- Option A: −3.68%
  To test, compute (1 + r)^6 with r = −0.0368. This is (0.9632)^6. Since 0.9632 is less than 1 but not dramatically, the sixth power would yield a factor somewhat less than 0.80, but the observed growth factor is 0.773. Without precise calculation, this value is plausible but would need checking; however, small deviations in r produce noticeable changes after six years. 
- Option B: 5.12%
  Here r = 0.0512, so (1 + r)^6 = 1.0512^6. This would produce a growth factor well above 1.3, not a decrease to 0.773. Therefore this positive return cannot match the observed decline from 281,000 to 217,200. It is inconsistent with the data.
- Option C: −4.20%
  With r = −0.042, we get (1 − 0.042)^6 = 0.958^6. A sixth power of a number just under 1 results in a sizable reduction, and 0.958^6 closely approximates 0.773, matching the observed ratio FV/PV. This aligns well with the given numbers.
- Option D: 4.39%
  r = 0.0439 gives (1.0439)^6, which would yield a growth factor greater than 1, again contradicting the fact that the final value is smaller than the initial investment. This cannot be correct for the observed outcome.
- Option E: −3.92%
  r = −0.0392 leads to (0.9608)^6. While this is a negative return, the exact sixth-power value would need calculation, but since −4.2% provides a closer match to the required 0.773 factor, this option is unlikely and would not fit as precisely as the −4.20% candidate.

An investor who was not as astute as he believed invested $281,000 into an account 6 years ago. Today, that account is worth $217,200. What was the annual rate of return on this account?

查看解析

登录即可查看完整答案

类似问题

A $1 investment made 10%, 20%, 30%, 10%, and 15% p.a returns in the first five years. What is the constant annual return for the five-year period that would have resulted in the same outcome at the end of Year 5 with compounded interest

Mr. Darden is selling his house for $200,000. He bought it for $164,000 ten years ago. What is the annual return on his investment?

Sara would like to evaluate the performance of her portfolio over the past 10 years. What compound annual rate of return has she achieved if she invested $12,000 10 years ago and now has $25,000?

Sara would like to evaluate the performance of her portfolio over the past 10 years. What compound annual rate of return has she achieved if she invested $12,000 10 years ago and now has $25,000?

You discover an antique in your attic that you purchased at an estate sale 10 years ago for $400. You auction it on eBay and receive $8,000 for your item. What annual rate of return did you earn?

What two functions can be used to calculate the compound annual growth rate

In a consumer society, many adults channel creativity into buying things

更多留学生实用工具

考试浏览器助手

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