Helen deposited $1200 at 5% interest compounded continuously. After 6 years, how much did she have ?
I got $2,160 but I was told it was incorrect
1200 * e^(.05*6) = 1619.83
too bad you didn't include your work ...
To calculate the amount of money Helen has after 6 years with continuous compounding, you can use the formula:
A = P * e^(rt),
Where:
A = The final amount of money
P = The original principal amount
e = The mathematical constant approximately equal to 2.71828
r = The interest rate (expressed as a decimal)
t = The time in years
In this case, Helen deposited $1200 at an interest rate of 5% (or 0.05) and the time is 6 years. Plugging these values into the formula, we get:
A = 1200 * e^(0.05*6)
Calculating this equation, we find:
A ≈ 1200 * e^(0.3)
A ≈ 1200 * 1.3498588075760032
A ≈ 1619.83
So, after 6 years of continuous compounded interest at a rate of 5%, Helen would have approximately $1619.83.
To find out how much Helen had after 6 years, we can use the formula for compound interest:
A = P * e^(rt)
Where:
A is the final amount
P is the principal amount (initial deposit)
e is the base of the natural logarithm (approximately 2.71828)
r is the annual interest rate (expressed as a decimal)
t is the time in years
In this case, Helen deposited $1200 at an interest rate of 5%, compounded continuously, for 6 years.
So, let's plug these values into the formula:
A = 1200 * e^(0.05 * 6)
Now, let's calculate it step by step:
1. Multiply the interest rate (0.05) by the time (6)
0.05 * 6 = 0.3
2. Add 1 to this result
1 + 0.3 = 1.3
3. Raise e to the power of this result
e^(1.3) ≈ 3.6692967
4. Multiply this result by the principal amount
1200 * 3.6692967 ≈ 4403.15
Therefore, after 6 years, Helen will have approximately $4403.15.
Please double-check your calculations to see if there was an error in the previous solution you provided.