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Sagot :
Answer:
Given that,
A wealthy businessman invests $10,000.
It expects a 6.75% rate of return annually.
To find: the number of years it take the investment to reach at least $15,000 in value.
Explanation:
we know that,
Amount invested at r% rate of interest after t years is,
[tex]A=P(1+\frac{r}{100})^t[/tex]where P is the initial investment.
Substitute the values we get,
[tex]15000=10000(1+\frac{6.75}{100})^t[/tex]we get,
[tex]\frac{3}{2}=1.0675^t[/tex][tex]1.5=1.0675^t[/tex]we get,
[tex]\log_{1.0675}(1.5)=t[/tex]Calculating this we get,
[tex]t=6.207[/tex]Round to the nearest number of years.
we get,
[tex]t=6[/tex]6 years will it take the investment to reach at least $15,000 in value.
Answer is: 6 years will it take the investment to reach at least $15,000 in value
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