121 Solve for rate or time

Bell:

1

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

1

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?

1

Solve for r.

1

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?

1

What is the rate?

1

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?

1

To solve, you will need to get rid of e.

rhetorical Q: What function (button) will do so?

Solve for the rate.

1

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?

1

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.

1

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?

1

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?

1

How long will it take?

1

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?

What is the equation?

1

How long will it take?

0

Choose all that are true

You can do the next 2 sections of DeltaMath.

Bell:

Notes L7-2b: Solving for Rate or Time

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?

Solve for r.

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?

What is the rate?

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?

To solve, you will need to get rid of e.rhetorical Q: What function (button) will do so?Solve for the rate.

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?

How long will it take?

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?

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?

How long will it take?

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?What is the equation?

How long will it take?

Choose all that are true

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?

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?

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?

To solve, you will need to get rid of e.

rhetorical Q: What function (button) will do so?

Solve for the rate.

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?

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?

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?

What is the equation?