Instructor comments in red italics.
Finance: Annuities
Use the given Savings Annuity Calculator and Payout Annuity Calculator Excel files to answer the following questions.
1. You deposit $50 into an IRA at the end of each month with a 6% APR for 15 years.
a. How much will you have at the end of 15 years?
b. Compare your total deposits to the accumulated value. How much did you deposit? How much interest accrued? The total deposits is simply the amount of deposit times the number of deposits. The interest accrued is found by taking the final amount in the annuity and subtracting the total deposits.
2. How much would you need to deposit at the end of every quarter into an IRA with an 8% APR in order to have $100,000 at the end of 20 years? This is determined by trial-and-error with the savings annuity calculator.
3. Suppose you deposit $200 every month into a traditional IRA with an APR of 9% for 30 years, but at the end of 5 years you withdraw $5000 (including penalties, fees, and taxes due on your withdrawn amount). How much money will you have lost over the next 25 years due to that one withdrawal? In the first worksheet in the savings annuity Excel file, students compute the amount in the annuity without a withdrawal. Then students find the amount in the annuity with the withdrawal. Subtract the two amounts.
4. From page 224 of Lippman’s second edition of Math in Society:
a. Suppose you invest $50 a month for 5 years into an account earning 8% compounded monthly. After 5 years, you leave the money, without making additional deposits, in the account for another 25 years. How much will you have in the end? Students use the second worksheet in the savings annuity Excel file that allows manual entry of all deposits. Students will simply stop making deposits after 5 years.
b. Suppose you put off making investments for the first 5 years, and instead made deposits of $50 a month for 25 years into an account earning 8% compounded monthly. How much will you have in the end? Students use the second worksheet in the savings annuity Excel file that allows manual entry of all deposits. Students make no deposits for the first 5 years, then $50 deposits for the remaining 25.
5. Suppose that you want to withdraw $3500 per month for 40 years after you retire at the age of 65 (just in case you end up a centenarian). Currently you are 30 years old and just start regular deposits into a new retirement account. Suppose your interest rate is 8%.
a. How much would you need in your retirement account at the time you retire for a payout annuity situation like this? This involves trial-and-error in the payout annuity calculator Excel file. Enter the given information and then experiment with different starting amounts.
b. Using your answer from part (a), how much would you need to deposit each month in your retirement account in order to achieve this goal? Now the students must use trial-and-error in the savings annuity calculator to accumulate the amount found in part (a).
c. Repeat part (b), but this time, assume that you start making deposits at the age of 25 rather than 30. Repeat part (b) except you have 5 more years to save.
6. Suppose you have saved $1,000,000 in your retirement account. Your plan is to retire at 65 and be able to make monthly withdrawals for 40 years.
a. If the interest rate is 4%, then what monthly withdrawal can you make?
b. If the interest rate is 5%, then what monthly withdrawal can you make?