Financial Planning For Mary: Retirement And Education Saving

Financial Planning for Mary Retirement and Education Savings Analysis

Financial Planning for Mary: Retirement and Education Savings Analysis

This report provides a comprehensive analysis of Mary’s financial situation as she approaches retirement. The primary focus is on applying time value of money (TVM) principles to evaluate various financial scenarios she faces. The analysis includes calculating the future value of her savings, the present value of her retirement bonus options, and the amount she needs to deposit annually to fund her granddaughter’s college education. Each of these issues involves straightforward calculations based on compound interest and annuity formulas, complemented by detailed explanations to clarify the reasoning behind each result.

Time value of money is a fundamental concept in finance that recognizes money available today is worth more than the same amount in the future due to its potential earning capacity. This principle underpins all the calculations in this report, from determining the growth of her savings to assessing the present value of future cash flows. Proper understanding of these concepts enables effective financial planning, ensuring that Mary can meet her retirement goals and support her granddaughter’s education.

Issue A: Future Value of Mary’s Savings Account

Mary has deposited $500 annually into her savings account for the last 19 years, with the account earning 5% interest compounded annually. She plans to make one additional deposit of $500 one year from today, after which she will close the account. The goal is to determine the total amount in the account at that time.

First, we recognize that the deposits form an ordinary annuity, with each deposit accruing interest over different periods. The future value of these 19 deposits can be calculated using the future value of an ordinary annuity formula:

FV of annuity = P × [( (1 + r)^n - 1 ) / r]

where:

- P = $500 (annual deposit)

- r = 5% or 0.05 (annual interest rate)

- n = 19 (number of deposits made so far)

Calculating the future value of these 19 deposits:

FV = 500 × [ ( (1 + 0.05)^19 - 1 ) / 0.05 ] ≈ 500 × [(2.517 - 1) / 0.05] ≈ 500 × 30.34 ≈ $15,170

Next, she will make one more $500 deposit one year from today, which will grow for one year:

Future value of the last deposit at the time of account closure:


FV = 500 × (1 + 0.05) = $525

Adding this to the accumulated value of previous deposits:

Total amount = $15,170 + $525 ≈ $15,695

Issue B: Present Value of Mary’s Bonus as a Lump Sum

Mary’s employer offers her a bonus of $75,000 annually for 20 years starting one year after her retirement. She prefers to receive a single lump sum payment immediately after retirement. To determine the equivalent lump sum, we need to calculate the present value of the deferred annuity using a 7% discount rate.

The present value of an annuity-immediate is:

PV = P × [ 1 - (1 + r)^-n ] / r

where:

- P = $75,000

- r = 7% or 0.07

- n = 20 years

Calculation:

PV = 75,000 × [ 1 - (1 + 0.07)^-20 ] / 0.07


≈ 75,000 × [ 1 - (1.07)^-20 ] / 0.07


≈ 75,000 × [ 1 - 0.26 ] / 0.07


≈ 75,000 × 10.57 ≈ $792,750

Thus, the lump sum equivalent of her bonus payments is approximately $792,750.

In comparing favorability, she essentially receives a one-time payment worth about $793,000 versus annual payments totaling $1.5 million. Given the discounting, the lump sum value is more advantageous if she plans to invest it, depending on her investment returns and needs.

Issue C: Present Value of Her Bonus for a Three-Year Extension

Because Mary has agreed to stay three additional years, the bonus payments will be deferred by this period. The question is, what is the current (present) value of her bonus if she chooses to accept the extension?

The present value of the remaining 20-year bonus starting one year from her retirement date is calculated as previously:

PV at retirement = $75,000 × [ 1 - (1 + 0.07)^-20 ] / 0.07 ≈ $792,750

However, since Mary will stay three more years, she effectively defers the receipt of these payments by 3 years. To find the present value at today’s date (i.e., her current time before extending her work), discount this PV back three years:

PV now = PV at retirement / (1 + 0.07)^3 ≈ 792,750 / 1.225 ≈ $647,367

Thus, the present value of her bonus, considering her extension, is approximately $647,367.

Issue D: Funding Future Education Expenses for Beth

Beth is currently 12 years old. She plans to start college at age 18 and will attend for 4 years. The current annual tuition is $11,000, expected to grow at 7% annually. Mary wants to pay half of her granddaughter’s tuition, starting at Beth’s 18th birthday, and make annual deposits today and each year until then. The account earns 4% annually, compounded.

First, project the future tuition costs at Beth’s starting year:

Future tuition at age 18:


= $11,000 × (1 + 0.07)^6 ≈ $11,000 × 1.503 ≈ $16,533

Half of this tuition (her intended contribution):

$16,533 / 2 ≈ $8,267

She will make annual deposits every year starting today until her granddaughter begins college, to fund these payments. The future value of these deposits must equal the present value of the total tuition costs at the start of Beth’s college. Since she’ll make deposits for 6 years (from now until age 18), we treat this as an ordinary annuity where each deposit grows at 4%, and we calculate how much she needs to deposit annually to amass the required amount:

First, determine the amount needed at age 18:

Total tuition for 4 years:


= $8,267 + ($8,267 × 1.07) + ($8,267 × 1.07^2) + ($8,267 × 1.07^3)


= Sum of a geometric series.

Calculating:

Year 1: $8,267


Year 2: $8,267 × 1.07 ≈ $8,845


Year 3: $8,845 × 1.07 ≈ $9,464


Year 4: $9,464 × 1.07 ≈ $10,112

Total tuition sum:

≈ $8,267 + $8,845 + $9,464 + $10,112 ≈ $36,688

Next, determine the present value of these future tuition payments at the time of Beth’s 18th birthday, discounted at 4%:

PV at age 18 = Sum of each tuition payment discounted to age 0:


= $8,267 / (1.04)^0 + $8,845 / (1.04)^1 + $9,464 / (1.04)^2 + $10,112 / (1.04)^3


≈ $8,267 + $8,509 + $8,771 + $9,119 ≈ $34,766

To accumulate this amount over six years of deposits at 4%, she needs to determine the annual deposit amount, D:

Using the future value of an ordinary annuity formula:


FV = D × [( (1 + r)^n - 1 ) / r]


We solve for D:


D = FV / [( (1 + r)^n - 1 ) / r]


where:


FV ≈ $34,766


r = 4% or 0.04


n = 6 years


D = 34,766 / [ (1.04)^6 - 1 ) / 0.04 ] ≈ 34,766 / [ 1.265 - 1 / 0.04 ] ≈ 34,766 / 6.32 ≈ $5,499

Therefore, Mary needs to deposit approximately $5,499 annually starting today to cover half of Beth’s tuition costs when she begins college.

Conclusion

This comprehensive analysis illustrates the importance of applying time value of money principles to manage various financial challenges effectively. By calculating the future value of her savings, evaluating the present value of her retirement bonus, and planning her contributions for her granddaughter’s education, Mary can make informed financial decisions aligned with her goals. Such calculations enable her to optimize her savings and investments, ensuring a financially secure retirement and supportive education funding for her granddaughter.

References

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