Suppose the government decides to issue a new savings bond that is guaranteed to

Question

Suppose the government decides to issue a new savings bond that is guaranteed to double in value if you hold it for 22 years. Assume you purchase a bond that costs $25 a. What is the exact rate of return you would earn if you held the bond for 22 years until b. If you purchased the bond for $25 in 2017 at the then current interest rate of 19 per c. In 2028, instead of cashing in the bond for its then current value, you decide to hold it doubled in value? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16) 19 year, how much would the bond be worth in 2028? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) the bond until it matures in 2039. What annual rate of return will you earn over the last 11 years? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a. Rate of return b. Value of bond c. | Rate of return

Explanation / Answer

a. To calculate the bond’s yield or rate of return, we have

Price P = $25

Maturity value M = $50 (double of base price)

Period n = 22 year

And rate of return or yield of the bond i =?

This government bond is like zero coupon bonds and there is only one cash flow from the bond at the time of maturity therefore the bond price can be calculated from the following formula

P = M/ (1+i) ^n

$25 = $50 / (1+i) ^22

Or i = 3.20 %

Therefore rate of return the bond is 3.20%

b. Price P = $25

Maturity value M (in 2028) =?

Period n = 11 year

And rate of return or yield of the bond i =0.19% per year

P = M/ (1+i) ^n

$25 = M / (1+0.19%) ^11

Or M = $25.53

Therefore the value of the bond is $25.53

c. Price P1 (in 2028) = $25.53

Maturity value M (in 2039) =$50

Period n = 11 year

And rate of return or yield of the bond i =?

P1 = M/ (1+i) ^n

$25.53 = $50 / (1+i) ^11

Or i = 6.30 %

Therefore rate of return the bond over last 11 years is 6.30%

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