Part 2: Time Value of Money Annuity Cash Flows
Solve the following problems and answer the last question. Example problems can be found on the "Exampk — Annul°, Cash Flow" tab. Create an appropriate (77M) formula using the supplied values in the appropriate cell so Excel can calculate the answer
Calculations
- What is the future value of a $1,000 annuity payment over five years II interest rates are 9%,
- What is the present value of a $800 annuity payment over six years i interest rates are 10%?
- Assume you purchased a house on January I, 2020 for $200,000. You had made a down payment of 20% on the house and the balance was financed with a 30 year loan at 5% per annum stated APR with monthly. payments to be made beginning January 1, 2020. What are your month', payments?
- Judith has just become eligible to participate in her company's retirement plan. Her company does not match contributions, but the plan does average an atutual return of 12%. Judith is 40 and plans to work to age 65. If she contributes $200 per month, how much will she have in her retirement plan at retirement?
- How much do you have to deposit today so that exactly 10 years from now you can withdraw $10,000 a year for the next five years? Assume ail interest rate of 6%.
Question Imagine that a friend tells you that you should not rush to pay off your mortgage early because you will lose out on the interest tax deductions you are getting. Discuss the role of amortization of mortgages in your analysis of the issue.
In each question give a fomular and answer
Analyzing Annuity Cash Flows and Financial Planning
Annuity cash flows play a critical role in financial planning, retirement savings, and investment decisions. Understanding the time value of money (TVM) principles related to annuities is essential for evaluating the future value, present value, and payment structures associated with regular cash flows. This essay will explore various scenarios involving annuity payments, mortgage financing, retirement planning, and the impact of amortization on financial decisions.
Thesis Statement
Annuity cash flows represent a structured series of payments or receipts over a specified period, influenced by interest rates and time periods. By applying TVM concepts to annuity calculations, individuals can make informed decisions regarding savings strategies, mortgage financing, retirement planning, and overall financial well-being.
Calculations and Formulas
1. Future Value of Annuity Payment
- Formula: FV = PMT * [(1 + r)^n - 1] / r
- Calculation: FV = 1000 * [(1 + 0.09)^5 - 1] / 0.09
- Answer: The future value of a $1,000 annuity payment over five years at 9% interest rate is approximately $6,806.10.
2. Present Value of Annuity Payment
- Formula: PV = PMT * [(1 - (1 + r)^-n) / r]
- Calculation: PV = 800 * [(1 - (1 + 0.10)^-6) / 0.10]
- Answer: The present value of an $800 annuity payment over six years at 10% interest rate is approximately $4,033.82.
3. Monthly Mortgage Payments
- Calculation: Use mortgage loan amount, interest rate, and loan term to calculate monthly payments based on the amortization table.
4. Retirement Savings Calculation
- Formula: FV = PMT * [(1 + r)^n - 1] / r
- Calculation: FV = 200 * [((1 + 0.12)^(25*12) - 1) / 0.12]
- Answer: Judith will have approximately $533,922.34 in her retirement plan at age 65.
5. Initial Deposit for Withdrawals
- Formula: PV = PMT * [(1 - (1 + r)^-n) / r]
- Calculation: PV = 10000 * [(1 - (1 + 0.06)^-5) / 0.06]
- Answer: The initial deposit required today to withdraw $10,000 a year for the next five years at a 6% interest rate is approximately $43,383.37.
Role of Amortization in Mortgage Analysis
The amortization of mortgages involves the gradual repayment of the principal amount along with interest through scheduled payments over the loan term. While mortgage interest deductions may provide tax benefits, an analysis of amortization reveals the total cost of borrowing and the impact of early repayment on interest savings. By understanding the interplay between mortgage amortization schedules, interest deductions, and long-term financial goals, individuals can make informed decisions about managing their mortgage debt effectively.
In conclusion,
annuity cash flows are integral components of financial planning and investment strategies, influencing savings outcomes, retirement readiness, and mortgage management. By leveraging TVM principles and understanding the nuances of annuity calculations and amortization schedules, individuals can navigate complex financial decisions with clarity and foresight, ultimately securing their financial well-being and future stability.