Aaron invested $7,000 in an account paying an interest rate of 3\tfrac{5}{8}% compounded continuously. Mia invested $7,000 in an account paying an interest rate of 3\tfrac{3}{4}% compounded monthly. After 17 years, how much more money would Mia have in her account than Aaron, to the nearest dollar?
Notes L7-2b: Solving for Rate or Time
Question 2
2.
Dominic is going to invest $1,800 and leave it in an account for 17 years. Assuming the interest is compounded annually, what interest rate, to the nearest tenth of a percent, would be required in order for Dominic to end up with $4,700?
What is the equation?
Question 3
3.
Solve for r.
Question 4
4.
Amelia is going to invest $90,000 and leave it in an account for 12 years. Assuming the interest is compounded monthly, what interest rate, to the nearest hundredth of a percent, would be required in order for Amelia to end up with $144,000?
What is the equation?
Question 5
5.
What is the rate?
Question 6
6.
Avery is going to invest $270 and leave it in an account for 20 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Avery to end up with $600?
What is the equation?
Question 7
7.
To solve, you will need to get rid of e.
rhetorical Q: What function (button) will do so?
Solve for the rate.
Question 8
8.
Tyler invested $350 in an account paying an interest rate of 4.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $700?
What is the equation?
Question 9
9.
How long will it take?
In the previous 2 examples, we used the ln function to elimnate e.
y=ln{x} is called the natural logarithm and is the inverse of the exponential funcion y=e^x.
We will use it solve for time (when the base isn't e). Then, we just have to ln both sides of the equation.
Question 10
10.
Example: Madeline invested $2,800 in an account paying an interest rate of 4.4% compounded annually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $6,100?
Question 11
11.
Aubree invested $4,400 in an account paying an interest rate of 2.4% compounded quarterly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $6,880?
What is the equation?
Question 12
12.
How long will it take?
Question 13
13.
Ella invested $4,900 in an account paying an interest rate of 3% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $5,920?