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 $50. a. What is the exact rate of return you would earn if you held the bond for 22 years until it doubled in value

r = 0.03200827973 or 3.200827973% rounded off to 3.20%

Explanation:

To calculate the rate of return provided by the bond such that the value of the bond doubles to $100, we will use the formula of future value of cash flow. The formula for future value of cash flow is as follows,

Future value = Present value * (1+r)^t

Where,

Plugging in the values for Future value, present value and t in the formula, we can calculate the r to be,

100 = 50 * (1+r)^22

100 / 50 = (1+r)^22

2 = (1+r)^22

Taking root of 22 on both sides.

(2)^1/22  =  (1+r)^22 * 1/22

1.03200828  =  1+r

1.03200828  -  1  =  r

r = 0.03200827973 or 3.200827973% rounded off to 3.20%

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