Acertain company recently sold five-year $1000 bonds with an annual yield of 9.75%. after how much time could they be sold for twice their original price? give your answer in years and months. (round your answer to the nearest month.

After 7 years and 5 months.

Step-by-step explanation:

Let x represent number of years.

We have been given that a certain company recently sold five-year $1000 bonds with an annual yield of 9.75%.

We can see that the value of bond is increasing exponentially, so we will use exponential growth formula to solve our given problem.

, where,

y = Final value,

a = Initial value,

r = Rate in decimal form,

x = Time

Substituting given values:

Since we need the selling price to be twice the original price, so we will substitute in above equation as:

Switch sides:

Take natural log of both sides:

Applying rule :

Since x represents time in years, so we need to convert decimal part into months by multiplying .4504 by 12 as 1 year equals 12 months.

7 years and 12*0.4504023 months = 7 years 5.4 months = 7 years 5 months

Therefore, after 7 years and 5 months the company could sold the bonds for twice their original price.

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