Part 1: Time Value of Money Single Cash Flow
Solve the following problems and answer the last question. Example problems can be found on the "Example Single Cash Flow" tab below. Create an appropriate (TVM) formula using the supplied values in the appropriate cell so Excel can calculate the answer.
Calculations
- How much would be in your savings account in 11 years after depositing S150 today, if the bat. pays 7, per year?
- A deposit of S350 earns the following interest rates: (a) 844, in the first year, (b) 6 in the second year, and (c) 5.5 in the third year. What would be the third year future value?
:iieedoimscpouutnettrahetepiress telt alue of an S850 payment made in 10 years when
- What annual rate of return is eamed on a S5,000 investment when it grows to 59,500 in five years?
- What is the rate of interest if your money doubles every 6 years? This is also known as Rule of 72.
Question 6. Given the same annual interest rate, would you rather have a savings account that paid interest compounded on a monthly basis, or one that compounded interest on an annual basis? Perform the calculation to support your answer.
In each question give a fomular and answer
Analyzing Time Value of Money and Investment Options
When considering financial decisions and investments, understanding the concept of the time value of money (TVM) is crucial. This essay will delve into the calculations and implications of single cash flows in the context of TVM, exploring scenarios of deposits, interest rates, future values, and compounding frequencies. By examining these calculations, we can gain insights into the growth and management of financial assets over time.
Thesis Statement
The time value of money plays a significant role in determining the worth of cash flows and investments over time. Through calculations and analysis of single cash flows, interest rates, future values, and compounding frequencies, individuals can make informed decisions regarding savings and investment strategies.
Calculations and Formulas
1. Savings Account Growth
- Formula: FV = PV * (1 + r)^n
- Calculation: FV = 150 * (1 + 0.07)^11
- Answer: The savings account would have $300.75 after 11 years.
2. Interest Earned over Three Years
- Calculation: FV = 350 + (350 * 0.08) + (350 * 0.06) + (350 * 0.055)
- Answer: The third year future value would be $417.95.
3. Future Value of $850 Payment in 10 Years
- Calculation: FV = 850 * (1 + r)^10
- Answer: The future value of an $850 payment made in 10 years depends on the interest rate.
4. Annual Rate of Return on a $5,000 Investment
- Calculation: Rate = [(FV/PV)^(1/n) - 1] * 100
- Calculation: Rate = [(9500/5000)^(1/5) - 1] * 100
- Answer: The annual rate of return earned on the $5,000 investment is 13.42%.
5. Rate of Interest for Doubling Money Every 6 Years (Rule of 72)
- Formula: Rate = 72 / Number of years to double
- Calculation: Rate = 72 / 6
- Answer: The rate of interest required for money to double every 6 years is approximately 12%.
Investment Options Comparison
6. Monthly vs. Annual Compounding- Formula for Monthly Compounding: FV_monthly = PV * (1 + r/12)^(12*n)
- Formula for Annual Compounding: FV_annual = PV * (1 + r)^n
- Calculation: Compare the future values of the two compounding options for a given interest rate.
In conclusion,
the time value of money serves as a fundamental concept in financial planning and investment decision-making. By applying TVM principles to single cash flows and investment scenarios, individuals can optimize their savings strategies and maximize returns on their investments. Understanding the impact of interest rates, compounding frequencies, and future values is essential for building wealth and achieving financial goals over time.