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Section 3.6 Worksheets Savings and Loans

Worksheet 3.6.1 Warmup for Section 3.4 and Section 3.5
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Exercise Group.

Write the letter of the graph that matches the type of interest.
1.
Simple Interest
2.
Compound Interest

3.

Write the letters in order from the type of compounding that would give the lowest amount to the type that would give the highest amount (assuming the same interest rate).

A. Quarterly

B. Continuously

C. Daily

D. Monthly

E. Annually

Exercise Group.

Write the letter of the formula that you would use to solve the problem. Complete the calculation using a spreadsheet.

Financial Formulas.

A. =P + P*rate*years

B. =FV(rate, nper, pmt, [pv], [type])

C. =PV(rate, nper, pmt, [fv], [type])

D. =P*exp(rate*years)

E. =effect(nominal rate, periods per year)

4.
You deposit $10,000 into an account that earns 5% interest, compounded quarterly, for 20 years.
5.
You loan a friend $1,000 for 2 years at 3% simple interest.
6.
You want to compare an account that earns 5.4% interest compounded daily with an account that earns 6.2% compounded quarterly.
7.
You deposit $7,000 into an account that earns 8% interest compounded continuously for 10 years.

Worksheet 3.6.2 In Class Activity for Section 3.4 and Section 3.5
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Group Activity

Use a spreadsheet to work on these problems. Write down the syntax to show your work. Answer each question in a complete sentence.

1.

Jackie is 34 years old. She would like to have one million dollars in her retirement account when she is 65 years old. How much would she need to deposit every month into an account with an APR of 7.25%, compounded monthly, to achieve her goal?

2.

If Jackie had started the account at age 21 (same APR), how much would she need to deposit every month to achieve her goal?

3.

If Jackie had started the account at age 21 (same APR) and deposited the amount calculated in Exercise 1 every month, what would the balance be when she retired at age 65?

4.

How much would Jackie need to deposit as a lump sum at age 21 with the same APR (without making another payment) to have a million dollars at age 65?

5.

Sam has a student loan of $30,000 at a fixed APR of 4.45%. If he wants to pay it off in 15 years, how much would he pay per month?

6.

How much would Sam pay in total?

7.

What percentage of the total was paid toward the loan amount of $30,000 and what percentage was paid toward interest?

8.

You want to buy a $350,000 home. You plan to put 10% down and take out a 30-year fixed mortgage on the rest. What will the loan amount be?

9.

What will your monthly payment be on your home mortgage if the interest rate is 4.5%?

10.

If you make all the payments on your home mortgage for 30 years, how much would you have paid for the house in total?

11.

In Exercise 9 above, what number would you get if you switch the 0 and the 315,000? Why are the answers so different? Explain the difference between these two scenarios.

Worksheet 3.6.3 Mortgage Lab
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This worksheet refers this Desmos page 16 .

1.

Set P equal to $130,000. What number does the area of the blue region correspond to?

2.

Try moving the r and Y sliders around. Does the area of the blue region tend to stay the same, get larger, or get smaller as you make these changes?

3.

Given what you know about how loans work, why would this be the case?

4.

Suppose you have a budget for $700 a month for a home. Also suppose that you can get an interest rate of 4%, and that you are looking for a 30 year loan. Move the Principle P around to find the maximum house price you can afford. What is it? For this question, you will get full credit as long as you are close enough. In order to get full credit, you need to be within $1,000 of the correct answer. Make sure that you factor in that you will have to make escrow payments.

5.

In the situation from the last exercise, what percentage of your money goes towards interest over the life of the loan?

6.

Use the same information from Exercise 4, but change the length of the loan to 15 years. Now what is the maximum house price you can afford? What now is the percentage of your money going towards interest?

7.

Given your answer to the exercise above, how would you explain to someone that a 15-year loan has less than twice the monthly payments of a 30 year loan?

8.

Keeping everything else constant, change the annual percentage rate r. Explain how a rising interest rate could be considered to make all home buyers a little poorer.

9.

Imagine that you have $4,000 in credit card debt, and you’d like to pay it off in 10 years. Your credit card company charges 20% on your debt. How much per month will you have to pay? (For this problem and problem 7 ignore the escrow payments).

10.

Given the credit card situation from the last exercise, how much will you have to pay if you try to pay it off in 5 years?

11.

Given your answer to the last two exercises, explain to your friend why it is important to pay credit card debt off as soon as possible.
https://www.desmos.com/calculator/1d0bkp9jh7