hannah invested $4000.How much money will she have in 15 years if the interest rate of 6% is being compounded continuously?
To calculate the amount of money Hannah will have in 15 years with continuous compounding, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A is the total amount of money after time t,
P is the principal amount (initial investment),
e is the mathematical constant approximately equal to 2.71828,
r is the interest rate as a decimal,
t is the time in years.
In this case, Hannah invested $4000 at an interest rate of 6% (or 0.06) and the time is 15 years. Plugging the values into the formula:
A = 4000 * e^(0.06 * 15)
Now, we can calculate the answer using the formula:
A ≈ 4000 * e^(0.9)
A ≈ 4000 * 2.4596
A ≈ 9838.40
Therefore, Hannah will have approximately $9838.40 in 15 years if the interest rate of 6% is compounded continuously.