Question

In March 2012, Daniela Motor Financing (DMF), offered some securities for sale to the public. Under the terms of the deal, DMF promised to repay the owner of one of these securities $1,000 in March 2037, but investors would receive nothing until then. Investors paid DMF $500 for each of these securities; so they gave up $500 in March 2012, for the promise of a $1,000 payment 25 years later.
a. Assuming that you purchased the bond for $500, what rate of return would you earn if you held the bond for 25 years until it matured with a value $1,000? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Rate of return _________ %
b. Suppose under the terms of the bond you could redeem the bond in 2022. DMF agreed to pay an annual interest rate of .9 percent until that date. How much would the bond be worth at that time? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.)
Bond value _________ $
c. In 2022, instead of cashing in the bond for its then current value, you decide to hold the bond until it matures in 2037. What annual rate of return will you earn over the last 15 years? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Rate of return ______ %

Answer 1

Answer:

A. 2.81%

B. $546.87

C.4.11%

Explanation:

A. Calculation for the rate of return

Rate of return= (1000/500)^(1/25)-1

Rate of return=2^(1/25)-1

Rate of return=1.0281-1

Rate of return= 0.0281*100

Rate of return= 2.81%

Therefore the Rate of return will be 2.81%

B. Calculation for How much would the bond be worth at that time

Bond value= (500*(1+0.009)^10)

Bond value= (500*(1.009%)^10)

Bond value=500*1.09373387

Bond value= $546.87

Note that 2012 to 2022 will give us 10 years.

Therefore Bond value will be $546.87

C. Calculation for what annual rate of return will you earn over the last 15 years

Return in last 15 years= (1000/546.87)^(1/15)-1

Return in last 15 years=1.828588^(1/15)-1

Return in last 15 years=1.0411-1

Return in last 15 years=0.0411*100

Return in last 15 years= 4.11%

Note that 2022 to 2037 will give us 15 years

Therefore the rate of return will be 4.11%