You deposit $3000 in an account earning 7% interest compounded continuously. The amount of money in the account after years is given by A(t)=3000 e^(0.07 t) .
How much will you have in the account in 5 years? $ Round your answer to 2 decimal places.
How long will it be until you have $17700 in the account? years. Round your answer to 2 decimal places.
How long does it take for the money in the account to double? years. Round your answer to 2 decimal places.
you have the formula. Just use your calculator, or any online calculator to find the values.
For #1, just plug in t=5
For #2, just solve
3000 e^(0.07t) = 17700
e^(0.07t) = 5.9
0.07t = ln 5.9
...
For #3, just solve
e^(0.07t) = 2
if you deposit $13,000 per year at 5% interest compounded annually, what will your balance be at the end of the 12th year?
Answers
To find the amount of money in the account after 5 years, we can use the formula A(t) = 3000e^(0.07t) where t represents the number of years.
1. Substitute t = 5 into the formula:
A(5) = 3000e^(0.07(5))
2. Evaluate the exponent:
A(5) = 3000e^(0.35)
3. Calculate the value of e^(0.35):
A(5) ≈ 3000 * 1.419
A(5) ≈ 4257
So, in 5 years, you will have approximately $4257 in the account.
Next, to find how long it will take to have $17700 in the account, we need to solve for t in the formula A(t) = 3000e^(0.07t) = 17700.
1. Divide both sides of the equation by 3000:
e^(0.07t) = 5.9
2. Take the natural logarithm of both sides to isolate t:
ln(e^(0.07t)) = ln(5.9)
0.07t = ln(5.9)
3. Solve for t by dividing both sides by 0.07:
t ≈ ln(5.9) / 0.07
t ≈ 5.90
So, it will take approximately 5.90 years to have $17700 in the account.
Finally, to determine how long it takes for the money in the account to double, we can use the doubling formula which is 2 times the initial amount:
1. Substitute A(t) = 2(3000) into the formula:
2(3000) = 3000e^(0.07t)
2. Simplify the equation:
2 = e^(0.07t)
3. Take the natural logarithm of both sides:
ln(2) = 0.07t
4. Solve for t by dividing both sides by 0.07:
t ≈ ln(2) / 0.07
t ≈ 9.90
So, it takes approximately 9.90 years for the money in the account to double.