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Midterm-WrittienAssignmentCompoundInterestSavingforRetirement.pdf
Math 25 Midterm: Saving for Retirement J. Frewing
On average, a mutual fund will earn about 7% interest compounded monthly in a long-term investment strategy. The key in planning for your financial future in retirement is to start early. Suppose you are a 22-year-old student and you wish to retire at age 65. That leaves 43 years for an initial investment to grow with compound interest.
1. (3 pt) Calculate how much an initial investment of $1,000 would grow in a mutual fund by the time you retire. (again, assume you are 22 years old for this calculation).
2. (3 pt) Calculate how much you will have in the account with an initial investment of
$5,000 at 22 years old?
3. Instead of investing a large amount of money at one time, you decide to deposit a fixed amount of money each month into an Individual Retirement Account (IRA).
a. (3 pt) Use the Ordinary Savings Annuity formula to calculate how much you would save if you deposit $50 each month into a mutual fund if you start making these deposits at the age of 22 and you want to retire at 65 years old. That formula is:
𝐴 = 𝑑 [(1 +
𝑟 𝑛 ) 𝑛𝑡
− 1]
𝑟 𝑛
where d is the fixed payment you save each month. Show how you would use the formula and Check your answer with the online calculator.
Math 25 Midterm: Saving for Retirement J. Frewing
b. (3 pt) What if you saved $100 each month?
c. (3 pt) How much would you have to save each month to wat $1,000,000 upon retirement*? (Again, assume 𝑡 = 43). Use both the formula and check your answer with an online calculator.
𝑑 = 𝐴(
𝑟 𝑛 )
(1 + 𝑟 𝑛 ) 𝑛𝑡
− 1
4. (3 pt) Now do a calculation for your personal scenario. Think about how many years you have until retirement, decide on a savings strategy (one-time investment or a savings annuity/sinking fund), and think about how much money you could realistically save (either a one-time investment or a fixed monthly payment).
5. (3 pt) Write a short summary of what you’ve learned about investing for retirement. Set
a one-year goal to save a certain amount to invest for your retirement.
