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Answer :
Time required to reach the principal amount $2000 to 10,000 dollars with 6 percent compounded continuously per year is equal to 26.8 years.
As given on the question,
Principal amount 'P' = 2,000 dollars
Interest rate 'r' = 6% compounded continuously per year
= 6/100
= 0.06
Amount 'A'= 10,000 dollars
Let 't' be the time taken.
Formula used:
t = ln(A/P) / r
Substitute the value we get,
t = ln(10,000/2000) / (0.06)
= 26.824 years
≈26.8 years
Therefore, time required for the given principal amount of dollars 2,000 to reach 10,000 dollars at the rate of interest 6% per year compounded continuously is equal to 26.8 years.
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