What was the annual return you earned on this investment? and Umass Capital Investments

What was the annual return you earned on this investment?

You purchase a high-yield, junk bond for $ 1,000 that pays $ 140 annually. After buying the bond, yields decline and you are able to reinvest the interest at only 9 percent. You reinvest all the interest payments.

What was the annual return you earned on this investment How much will you have when the bond is retired after 12 years?


Investment best answer:

Answer by Sumant
Calculating the Rate of Return on Investments

Let's say you invest $ 100 in stock, which is called your capital. One year later, your investment yields $ 110. What is the rate of return of your investment? We calculate it by using the following formula:

((Return - Capital) / Capital) × 100% = Rate of Return

Therefore,

(($ 110 - $ 100) / $ 100) × 100% = 10%

Your rate of return is 10%.
There are two ways to measure the rate of return on an investment.

Average annual rate of return (also known as average annual arithmetic return)
Compound rate of return (also called average annual geometric return)

You initially invest $ 100. One year later, your investment grows to $ 200 in value. The year after that, the investment drops back to $ 100. The rate of return after the first year is

((Return - Capital) / Capital) × 100% = Rate of Return

(($ 200 - $ 100) / $ 100) × 100% = 100%

The rate of return after the second year is

(($ 100 - $ 200) / $ 200) × 100% = -50%

By using the formulas for calculating the average annual rate of return, we get a percentage that measures gains accurately over only a short period. Whereas, the geometric or compound rate of return is a better yardstick to measure your investment over the long run. The arithmetic mean or average return should be used to calculate return on investment only in the short-term.

Average annual return (arithmetic mean) = (Rate of Return for Year 1 + Rate of Return for Year 2) / 2 = (100% + (-50%)) / 2 = 25% (Arithmetic return = 25%)

Compound return (geometric mean) = (capital / return) ^ (1 / n) - 1 where n = number of years. The formula is (100 / 100) ^ .5 - 1 = 0%. (Geometric return)

Investment

Umass Capital Investments


Image by Office of Governor Patrick
Tuesday, October 2, 2012 – Governor Deval Patrick announced significant capital investments in the UMass system, furthering the Patrick-Murray Administration's commitment to building an affordable, world-class system of public higher education in Massachusetts. The Governor made the announcement at UMass Boston as President Caret and other university leaders marked the system's 150th anniversary. The Governor noted that the 7 million in new bond funding will advance high-quality instructional and research facility projects throughout the UMass system so that the Commonwealth can compete in a 21st Century knowledge-based economy.

(Photo: Eric Haynes / Governor's Office)

---

Orignal From: What was the annual return you earned on this investment? and Umass Capital Investments