A Young Engineer Decides To Save $240 Per Year For Retiremen ✓ Solved

A young engineer decides to save $240 per year toward retir

Activity I: A young engineer decides to save $240 per year toward retirement in 40 years. If he invests this sum at the end of every year at 9%, then how much will be accumulated by retirement time? If by astute investing the interest rate could be raised to 12%, then what sum could be saved? If he deposits one fourth of this annual amount each quarter ($60 per quarter) in an interest bearing account earning a nominal annual interest rate of 12%, compounded quarterly, how much could be saved by retirement time? In part (c), then what annual effective interest rate is being earned?

Activity II: Maurice Micklewhite has decided to replant his garden. Show him what the cost is of making an erroneous decision at various stages of the project, starting with conceptual design and ending with the ongoing maintenance of the garden.

Paper For Above Instructions

### Introduction

The objective of this paper is to analyze two distinct financial scenarios: the retirement savings plan of a young engineer and the cost implications of decision-making for Maurice Micklewhite's gardening project. Through mathematical calculations and conceptual frameworks, we aim to provide clear insights into retirement savings growth and the financial consequences of poor planning in gardening.

### Part I: Retirement Savings Analysis

#### Future Value of Retirement Savings at 9%

The young engineer aims to save $240 annually for 40 years, investing at an interest rate of 9%. The future value (FV) of this annuity can be calculated using the future value of an annuity formula:

FV = P * [{(1 + r)^n - 1} / r]

Where:

P = annual payment ($240)

r = annual interest rate (9% or 0.09)

n = number of years (40)

Substituting the values:

FV = 240 * [{(1 + 0.09)^40 - 1} / 0.09]

FV = $240 * [{(1.09)^40 - 1} / 0.09]

Calculating (1.09)^40, we get approximately 31.409. Thus:

FV ≈ 240 * [{31.409 - 1} / 0.09]

FV ≈ 240 * [30.409 / 0.09]

FV ≈ 240 * 337.876 = $81,049.50

Therefore, the total savings accumulated by retirement time at a 9% interest rate would be approximately $81,049.50.

#### Future Value of Retirement Savings at 12%

If investment opportunities allow for a 12% interest rate instead, we can apply the same annuity formula:

FV = P * [{(1 + r)^n - 1} / r]

Substituting:

FV = 240 * [{(1 + 0.12)^40 - 1} / 0.12]

FV = $240 * [{(1.12)^40 - 1} / 0.12]

(1.12)^40 is approximately 93.515, so:

FV ≈ 240 * [{93.515 - 1} / 0.12]

FV ≈ 240 * [92.515 / 0.12]

FV ≈ 240 * 771.28 = $185,030.82

Thus, if the interest rate is raised to 12%, the total savings at retirement would be around $185,030.82.

#### Impact of Quarterly Savings

If the engineer deposits a quarter of his annual amount quarterly—$60 per quarter—at a 12% nominal annual interest rate compounded quarterly. The future value of these quarterly payments can be calculated using the future value of an ordinary annuity formula, modified for quarterly compounding:

FV = P * [{(1 + r/m)^(nt) - 1} / (r/m)]

Where:

P = quarterly payment ($60)

r = nominal annual interest rate (0.12)

m = number of compounding periods per year (4)

t = total period in years (40)

Substituting the real values into the equation:

FV = 60 [{(1 + 0.12/4)^(440) - 1} / (0.12/4)]

FV = 60 * [{(1 + 0.03)^(160) - 1} / 0.03]

(1.03)^160 is approximately 39.885, so:

FV ≈ 60 * [{39.885 - 1} / 0.03]

FV ≈ 60 * [38.885 / 0.03]

FV ≈ 60 * 1296.167 = $77,769.61

Consequently, the total savings by retirement time when depositing quarters at a nominal interest rate of 12% compounded quarterly would be approximately $77,769.61.

#### Effective Annual Interest Rate (EAIR)

To determine the annual effective interest rate being earned from quarterly compounding at a nominal rate of 12%, we can use the formula:

EAIR = (1 + r/m)^(m) - 1

Substituting the values:

EAIR = (1 + 0.12/4)^(4) - 1

EAIR = (1 + 0.03)^(4) - 1

EAIR ≈ 1.1255 - 1 = 0.1255 or 12.55%

This means that the effective annual interest rate earned is approximately 12.55%.

### Part II: Cost of Erroneous Decisions in Gardening

For Maurice Micklewhite's gardening project, understanding the costs associated with erroneous decisions is crucial to managing budget allocations effectively. Cost implications can arise at various stages, such as:

#### 1. Conceptual Design

Erroneous planning at this stage can lead to miscalculations regarding garden layout, plant selection, and resource estimation. A poor choice may result in higher expenses down the line due to redesign or modifications needed to address unforeseen problems.

#### 2. Procurement

Choosing the wrong suppliers or inadequate materials can incur additional costs and potential project delays. A reputable supplier may charge more upfront but ensure quality and longevity, avoiding future spending.

#### 3. Execution and Installation

When the garden is being established, poor decisions about planting techniques or timelines, such as incorrect planting seasons, can diminish plant health, requiring further investment to replace dead or damaged plants.

#### 4. Maintenance

Long-term maintenance requires an understanding of sustainable practices. Deficient choices regarding fertilizer use or pest control can escalate expenses and erode budget forecasts.

### Conclusion

In summary, thoughtful planning for retirement through consistent savings and carefully considering each phase of gardening development can lead to substantial financial benefits. The analysis presented here illustrates the importance of financial literacy and informed decision-making in both personal finance and project management.

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