BUSA 3200 Worksheet On Interest And Mortgage Loans

BUSA 3200 Worksheet On Interest And Mortgage Loans

This assignment involves calculating the potential growth of lottery winnings over time, understanding interest accumulation, evaluating retirement income possibilities with annuities, and analyzing mortgage options based on projections and real estate investment decisions. Students will also be required to make a reasoned choice between paying cash or taking out a mortgage for a house purchase, considering associated risks and benefits.

Paper For Above instruction

The scenario set forth involves a person who has recently won a substantial lottery prize of $219,303. The primary objective is to evaluate the financial implications of this windfall, including converting it into an investment, projecting its growth over 30 years, and analyzing the impact of interest rates and mortgage options on their financial future. This comprehensive analysis encompasses future value calculations, interest earnings, retirement planning through annuities, and mortgage payment assessments, culminating in a strategic decision-making process regarding real estate financing.

Financial Growth of Lottery Winnings and Investment Planning

The initial step involves determining the investable amount—$219,303—and selecting an expected annual rate of return on this investment. The rate of return is a vital estimate, reflective of expected market performance, risk tolerance, and investment type. For example, investing in diversified mutual funds or stocks generally yields an average annual return around 7-8%, whereas more conservative bonds might yield around 3-5%. The student should justify their chosen rate based on personal risk appetite and historical market data.

Assuming the individual selects a conservative 6% annual return, the future value of the investment after 30 years can be calculated using the formula for compound interest:

\[ FV = PV \times (1 + r)^n \]

where PV is the present value, r is the annual rate of return, and n is the number of years. Applying the values:

\[ FV = 219,303 \times (1 + 0.06)^{30} \]

resulting in a projected asset value that exceeds $1 million, illustrating significant growth potential over time if the expected return is realized.

The total interest earned over the 30-year period can be derived by subtracting the original principal from the final amount:

\[ Total \, Interest = FV - PV \]

which roughly equates to a $1 million-plus gain, highlighting the power of compounded growth in long-term investments. Calculating the average annual interest earned provides insight into the investment’s performance consistency.

Retirement Income via Annuities

With the accumulated savings, the scenario explores the possibility of retiring after 30 years and converting the lump sum into an annuity paying a 5% annual interest rate. The annuity would provide a fixed income stream over the subsequent 30 years, which can be calculated using the present value of an annuity formula:

\[ P = \frac{FV \times r}{(1 - (1 + r)^{-t})} \]

where P is the annual withdrawal, FV is the total accumulated amount, r is the annual interest rate, and t is the number of years in retirement.

This calculation produces an annual withdrawal amount it would be possible to sustain based on the investment’s growth, ensuring the retiree can plan their finances with confidence. For instance, if the accumulated fund exceeds $1 million, the annual payout at a 5% rate would be approximately $50,000, adjusted for inflation and other factors.

Real Estate Purchase: Cash Payment Versus Mortgage

In the next phase, the individual considers purchasing a house that costs exactly the amount saved—$219,303—either by paying cash or financing via a mortgage. The current 30-year mortgage rate assumed is 4.5%. The monthly mortgage payment can be calculated using the standard mortgage formula:

\[ M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1} \]

where P is the loan amount, r is the monthly interest rate, and n is the total number of payments.

Calculating for a $219,303 loan at 4.5% annual interest over 30 years yields a monthly payment that, when multiplied by 360 months, results in the total repayment amount. Total interest paid over the life of the loan can then be derived by subtracting the original principal from the total paid amount, illustrating how mortgage payments include both principal and interest. This analysis helps compare the total costs of buying with cash versus leveraging debt.

Deciding whether to pay cash or finance is complex. Paying cash avoids interest payments and debt obligations, providing immediate ownership; however, it depletes liquidity that could have been invested elsewhere for returns exceeding mortgage costs. Conversely, taking a mortgage preserves cash flow, allowing for investments that could potentially outperform the interest rate of 4.5%, but introduces risk if interest rates increase or if market values decline.

Decision-Making and Risk Analysis

Finally, the decision involves weighing the benefits of liquidity and potential higher returns against the costs and risks of debt. Paying cash eliminates monthly mortgage payments and reduces financial stress, but may limit investment flexibility. Financing the house allows for maintaining diversified investments; however, it exposes the homeowner to interest rate fluctuations, potential repayment burdens, and market risk associated with real estate depreciation.

The choice hinges on personal risk tolerance, investment acumen, and market outlook. For example, if the individual's investments are projected to outperform the mortgage interest rate, financing might be preferable. Conversely, a conservative approach or uncertain market conditions might favor paying cash for peace of mind and lower total costs.

In conclusion, strategic financial planning requires evaluating long-term growth, retirement security, and current real estate options within the context of one's risk appetite and market conditions. Making informed decisions based on detailed calculations and realistic projections can optimize financial outcomes and provide peace of mind for future years.

References

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