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Answer:
Using continuous interest 6.83 years before she has $1600.
Using continuous compounding, 6.71 years.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.
Continuous compounding:
The amount of money earned after t years in continuous interest is given by:
In which P(0) is the initial investment and r is the interest rate, as a decimal.
If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600?
We have to find t for which when
Using continuous interest 6.83 years before she has $1600
If the compounding is continuous, how long will it be?
We have that
Then
Using continuous compounding, 6.71 years.