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 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.) 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.) c. In 2028, instead of cashing in the bond for its then current value, you decide to hold 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. What is the exact rate of return you would earn if you held the bond for 22 years until it doubled in value?

FV = PV x (1 + r )t

r = (FV / PV) 1/t – 1

r = (50/25)1/22 – 1 = (2) 1/22 – 1 = 1.0320 – 1 = 0.0320 or 3.20%   

b.   If you purchased the bond for $25 in 2017 at the then current interest rate of .19 per year, how much would the bond be worth in 2028?

FV = PV × (1+r )t = 25 × (1 + 0.0019) (2028–2017) = 25 × (1.0019)11

= 25 × 1.0211 = $25.53   

c.   In 2028, instead of cashing in the bond for its then current value, you decide to hold the bond until it matures in 2039. What annual rate of return will you earn over the last 11 years?

r = (FV / PV)1/t – 1 = (50 / 25.53)1/11 – 1 = (1.9585)1/11 – 1

= 1.0630 – 1 = 0.0630 or 6.30%

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