Q.1.Differentiate future value from present value and explain how compound interest differs from simple interest.

Q.2. John expects to need $50,000 as a down payment on a house in six years. How much does she need to invest today in an account paying 7.25 percent?
Q.3. Richard is planning to invest $25,000 today in a mutual fund that will provide a return of 8 percent each year. What will be the value of the investment in 10 years?
Q.4.What do you mean ratio analysis? Discuss important ratios used for analyzing financial statements.
Q.5.How do an ordinary annuity, an annuity due, and a perpetuity differ? Explain.

Q1. To understand the difference between future value and present value, you need to understand the concept of time value of money. The time value of money states that the value of money today is worth more than the same amount of money in the future due to the opportunity cost of having that money available for use now.

- Future value: Future value refers to the value of an investment or a sum of money at a specific point in the future, based on a certain interest rate. It calculates how much an investment will grow to over a given time period if it earns interest. Future value accounts for the compounding of interest, where interest earned in one period is added to the initial investment and then earns interest itself in subsequent periods.

- Present value: Present value, on the other hand, represents the current value of a future payment or investment, discounted at a given interest rate. It allows you to determine the value of an amount that you will receive or have to pay in the future, in today's dollars. Present value takes into account the time value of money, adjusting the future cash flows by discounting them to reflect their current worth.

Compound interest differs from simple interest in how the interest is calculated and added to the investment:

- Simple interest: With simple interest, interest is calculated only on the initial principal amount. The interest earned remains constant over the investment period, regardless of how many times the interest is applied.

- Compound interest: Compound interest takes into account the accumulation of interest on the initial principal amount as well as any previously earned interest. The interest is compounded, meaning it is reinvested and added to the investment at regular intervals. This results in interest being earned on the interest, leading to exponential growth. Compound interest can significantly increase the final value of an investment over time.

Q2. To calculate how much John needs to invest today, we can use the formula for present value:

Present Value = Future Value / (1 + Interest Rate)^n

In this case, the future value (the down payment on the house) is $50,000, the interest rate is 7.25% (convert it to decimal form: 0.0725), and the time period is 6 years (n = 6).

Plugging in these values into the formula:

Present Value = $50,000 / (1 + 0.0725)^6
Present Value = $50,000 / (1.0725)^6
Present Value = $50,000 / 1.584874

So, John needs to invest approximately $31,565.91 today in an account paying 7.25 percent.

Q3. To calculate the value of Richard's investment in 10 years, we can use the future value formula:

Future Value = Present Value * (1 + Interest Rate)^n

In this case, the present value is $25,000, the interest rate is 8% (convert it to decimal form: 0.08), and the time period is 10 years (n = 10).

Plugging in these values into the formula:

Future Value = $25,000 * (1 + 0.08)^10
Future Value = $25,000 * (1.08)^10
Future Value = $25,000 * 1.913734

So, the value of Richard's investment in 10 years will be approximately $47,843.35.

Q4. Ratio analysis is a technique used in financial analysis to evaluate the relationships between different financial statement items. It involves comparing various ratios derived from financial statements to assess a company's financial health and performance.

There are several important ratios used in ratio analysis. Here are a few examples:

- Liquidity ratios: These ratios measure a company's ability to meet short-term obligations. Examples include the current ratio (current assets divided by current liabilities) and the quick ratio (quick assets divided by current liabilities).

- Profitability ratios: These ratios assess the company's ability to generate profits. Examples include the gross profit margin (gross profit divided by sales) and the return on equity (net income divided by shareholders' equity).

- Debt ratios: These ratios analyze the company's leverage or debt levels. Examples include the debt-to-equity ratio (total debt divided by total equity) and the interest coverage ratio (earnings before interest and taxes divided by interest expense).

- Efficiency ratios: These ratios evaluate how efficiently the company utilizes its assets. Examples include the asset turnover ratio (sales divided by average total assets) and the inventory turnover ratio (cost of goods sold divided by average inventory).

These ratios, and many others, help provide insights into various aspects of a company's financial performance and help in making informed decisions.

Q5. An ordinary annuity, an annuity due, and a perpetuity differ in terms of payment timing and duration:

- Ordinary annuity: An ordinary annuity refers to a series of equal cash flows or payments that occur at the end of each period. The first payment is made at the end of the first period, and subsequent payments are made at the end of each subsequent period.

- Annuity due: An annuity due is similar to an ordinary annuity, but the payments are made at the beginning of each period, rather than at the end. The first payment is made at the beginning of the first period, followed by payments at the beginning of each subsequent period.

- Perpetuity: A perpetuity is an annuity that lasts indefinitely, with payments continuing forever. Unlike a regular annuity, there is no specific end date for a perpetuity.

The key difference between these three types of annuities is the timing of the cash flows. In an ordinary annuity, payments are made at the end of the periods, in an annuity due, payments are made at the beginning of the periods, and in a perpetuity, payments continue indefinitely into the future.