Suppose Johnny invests $2,745 into an account, which has been earning interest for many years and he now has a total of $39,974.
1 answer:
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Answer:
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.