Naomi Dexter is 20 years old and attends Southwest Tennessee Community College. Her Business English instructor asked her to make a report detailing her plans

Naomi Dexter is 20 years old and attends Southwest Tennessee Community College. Her Business English instructor asked her to make a report detailing her plans for retirement. Naomi decided she would investigate several ways to accumulate $1 million by the time she retires. She also thinks she would like to retire early when she is 50 years old so she can travel around the world. She is considering a long-term certificate of deposit (CD) that pays 3% annually, and an annuity that returns 6% annually. She also did a little research and learned that the average long-term return from stock market investments is between 10% and 12%. Now she needs to calculate how much money she will need to deposit each year to accumulate $1 million.

1. If Naomi wants to accumulate $1,000,000 by investing money every year into her CD at 3% for 30 years until retirement, how much does she need to deposit each year?

2. If she decides to invest in an annuity that returns at 6% interest, how much will she need to deposit annually to accumulate the $1,000,000?

3. If Naomi invests in a stock portfolio, her returns for 10 or more years will average 10%-12%. Naomi realizes that the stock market has higher returns because it is a more risky investment than a savings account or a CD. She wants her calculations to be conservative, so she decides to use 8% to calculate possible stock market earnings. How much will she need to invest annually to accumulate $1,000,000 in the stock market?

4. After looking at the results of her calculations, Naomi has decided to aim for $500,000 savings by the time she retires. She expects to have a starting salary after college of $25,000 to $35,000 and she has taken into account all of the living expenses that will come out of her salary. What will Naomi's annual deposits need to be to accumulate $500,000 in an investment at 6%?

5. If Naomi decides that she will invest $3,000 per year in a 6% annuity for the first ten years, $6,000 for the next ten years, and $9,000 for the next ten years, how much will she accumulate? Treat each ten-year period as a separate annuity. After the ten years of an annuity, then it will continue to grow at compound interest for the remaining years of the 30 years.

Step by Step Solution

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Step: 1

To accumulate 1000000 by investing money every year into her CD at 3 for 30 years until retirement Naomi can use the formula for the future value of an annuity FV PMT x 1 rn 1 r where FV is the future value PMT is the payment amount r is the interest rate per period and n is the number of periods In this case Naomi wants to accumulate 1000000 r is 3 and n is 30 years Plugging in these values we get 1000000 PMT x 1 00330 1 003 Solving for PMT we get PMT 1013870 Therefore Naomi needs to deposit 1013870 per year into her CD at 3 for 30 years to accumulate 1000000 by retirement If Naomi decides to invest in an annuity that returns at 6 interest she can use the same formula as above but with r 6 1000000 PMT x 1 00630 1 006 Solving for PMT we get PMT 700322 Therefore Naomi needsto deposit 700322 per year into the annuity at 6 for 30 years to accumulate 1000000 by retirement If Naomi invests in a stock portfolio with an average return of 8 she can use the formula for future value of an annuity as well 1000000 PMT x 1 00830 1 008 Solving for PMT we get PMT 453198 Therefore Naomi needs to deposit 453198 per year into the stock portfolio with an average return of 8 for 30 years to accumulate 1000000 by retirement If Naomi has decided to aim for 500000 savings by retirement instead she can use the same formula for future value of an annuity 500000 PMT x 1 00630 1 006 Solving for PMT we get PMT 400552 Therefore Naomi needs to deposit 400552 per year into the investment at 6 for 30 years to accumulate 500000 by retirement If Naomi decides to invest 3000 per year in a 6 annuity for the first ten years 6000 for the nextten years and 9000 for the next ten years she can treat each tenyear period as a separate annuity and calculate the future value for each one using the annuity formula For the first ten years FV1 3000 x 1 00610 1 006 FV1 3806123 For the second ten years FV2 6000 x 1 00610 1 006 FV2 9515309 For the third ten years FV3 9000 x 1 00610 1 006 FV3 18261472 After the third tenyear period the accumulated value will continue to grow at 6 annually for the remaining 10 years until retirement To calculate the future value at the time of retirement we can use the formula for the future value of a ... blur-text-image