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Math OER
Week 3 Activity

Practice with Annuities

Show your work or explain your thinking. There may be a few different methods that work.

1a. Amina set up a retirement account. She will have $50 taken out of each of her fortnightly paychecks (k = 26). Her account will earn 7% interest. She just had her 30th birthday, and she plans to retire at age 65. Find the balance in her account at the end of the 35 years.

1b. Find Amina's total contribution to the account.

1c. Find the total interest Amina will earn.

2a. Mr. and Mrs. Abassi set up an IRA to save for their retirement. They will deposit $250 from each of Mrs. Abassi's twice-monthly paychecks. Their account will earn 5% interest. How much will they have in their account after 30 years?

2b. After 30 years, the Abassis retire. They convert their annuity to a savings account, which earns 4% interest compounded monthly. At the end of each month, they withdraw $1,800 for living expenses. Complete the chart below for their post-retirement account.

2c. What will happen to their account balance if they continue this process?

3a. Jeanne and Harold Kimura want to save $750,000 for retirement. Thanks to their employers, they have access to a tax-deferred retirement account that earns 8% interest, compounded monthly. If they have 40 years to save, how much do they need to deposit each month?

3b. How much of the $750,000 they will have will be from contributions? From interest?

3c. The Kimuras are interested in retiring early. How much would they have to deposit each month to reach the same goal in just 25 years?

3d. If they retire in 25 years as in part (c), how much of their account balance is from interest?

3e. The final question they have is whether $750,000 is "enough" for retirement. Identify what pieces of information you would need in order to be able to answer this question for them.

Practice with Loans

1. Shelby and Natalie Kersting want to buy a house. They are looking at a house that costs $145,000, and they will also need to pay 3% of the house purchase price in closing costs. Find the total amount of money they will borrow if they finance the entire cost plus closing cost.

2a. The Kerstings have two options for a home loan. The first option is a 15-year loan that has an annual interest rate of 4.5%. How much would their monthly payment be (principal and interest)?

2b. With this first option, how much would they pay in all, over the course of the loan?

2c. How much of your answer to part (2b) is interest?

3a. The second option is a 30 year loan with an annual interest rate of 5.5%. How much would their monthly payment be (principal and interest)? (Banks tend to have higher interest rates on longer loans due to risk.)

3b. With this second option, how much would they pay in all, over the course of the loan?

3c. How much of your answer to part (3b) is interest?

4. Which option costs less in interest? How much interest does that option save?

5. What are some advantages of taking the option that costs more in interest?

6a. The Kerstings think about each month setting aside the difference between the monthly payment options as retirement money. How much would they be saving each month?

6b. If they can save that money in a money market account earning 7% per year (annually, after taxes), how much would they have at the end of 30 years? (Hint: you will need a different formula than you used for the loan calculations.)

6c. Does this amount of money make up for the extra interest they had to pay?

7. Finally, with everything you know about the Kerstings and their options, which option would you recommend for them?

Practice with Formulas

First decide which type of problem it is. Then solve the problem.

1. You have $500,000 saved for retirement. Your account earns 5% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?

2. You deposit $2000 into an account earning 4% interest compounded monthly. How much will you have in 25 years?

3. José has determined he needs to have $800,000 for retirement in 30 years. His account earns 7% interest. How much does he need to deposit each month to meet his goal?

4. You want to buy a $10,000 car. The company is offering a 3% interest rate for 36 months (3 years). What will your monthly payments be?

5. How much would you need to deposit in an account now to have $6,000 in the account in 8 years? Assume the account earns 6% interest. List any other assumptions you make.

6. You want to be able to withdraw $8,000 each quarter for the next 5 years. Your account earns 8% interest. How much do you need in your account at the beginning to make this happen?

7. Challenge Question Mike plans to make contributions to his retirement account for 15 years. After the last contribution, he will start withdrawing $10,000 each quarter for 10 years. Assuming Mike’s account earns 8% interest compounded quarterly, how large must his quarterly contributions be during the first 15 years, in order to accomplish his goal?

These problems are not graded. They are only to help you practice with our math topics. Do not rush to look at answers! First ask for hints from your instructor or classmates. But if you are really ready, the answers are here.