Finance Basics: Interest and Present Value
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Questions and Answers

What is the future value of an ordinary annuity if the monthly payment is $200, the interest rate is 6% per annum, and the investment lasts for 5 years?

  • $15,000.00
  • $12,345.67
  • $14,774.38 (correct)
  • $10,256.34

Which of the following accurately describes the variable 'r' in the future value formula for an ordinary annuity?

  • Monthly interest rate (correct)
  • Total duration in months
  • Annual interest rate
  • Total payment amount

What is the primary function of a sinking fund?

  • To reduce interest rates on debts
  • To provide emergency cash reserves
  • To increase company profits annually
  • To accumulate funds for specific future liabilities (correct)

Which statement best defines 'liquidity' in financial terms?

<p>It indicates how quickly an asset can be converted to cash. (C)</p> Signup and view all the answers

In the context of the ordinary annuity formula, what does 'n' represent?

<p>The number of payment periods (D)</p> Signup and view all the answers

How much will an investment of $1,000 grow to after 3 years at an annual interest rate of 5% compounded annually?

<p>$1,157.63 (A)</p> Signup and view all the answers

What is the formula used to calculate the effective annual rate (EAR) from a nominal interest rate?

<p>EAR = (1 + r/n)^n - 1 (A)</p> Signup and view all the answers

If you take a loan of $5,000 at 8% annual simple interest for 2 years, what will be the total amount to repay?

<p>$5,800 (C)</p> Signup and view all the answers

To find the present value of $10,000 due in 5 years with a 7% discount rate compounded annually, which formula should you use?

<p>PV = FV / (1 + r)^t (D)</p> Signup and view all the answers

Which of the following statements about annuities is false?

<p>Annuities can have unlimited terms. (C)</p> Signup and view all the answers

What is the future value of an ordinary annuity that makes annual payments of $1,000 at an interest rate of 5% over 10 years?

<p>$13,207.57 (B)</p> Signup and view all the answers

How do you calculate interest if you take a loan of $5,000 at an 8% annual simple interest for 2 years?

<p>Interest = Principal x Rate x Time (B)</p> Signup and view all the answers

What concept does the term 'effective annual rate' refer to in finance?

<p>The actual rate of interest earned after compounding is taken into account. (B)</p> Signup and view all the answers

What is the future value of an ordinary annuity that pays $1,000 annually for 10 years at a 5% interest rate?

<p>$13,207.57 (A)</p> Signup and view all the answers

What formula is used to calculate monthly loan payments?

<p>PMT = P * r / (1 - (1 + r)^-n) (A)</p> Signup and view all the answers

How is the Rule of 72 applied in finance?

<p>To estimate how long it takes for an investment to double (C)</p> Signup and view all the answers

If an investment is compounded continuously, which formula is applied?

<p>FV = PV * e^(rt) (C)</p> Signup and view all the answers

What is the calculated equity if a company's total assets are $500,000 and total liabilities are $300,000?

<p>$200,000 (D)</p> Signup and view all the answers

What is the present value of an annuity due that pays $2,000 annually for 5 years at a 6% discount rate?

<p>$9,649.46 (C)</p> Signup and view all the answers

What does the debt-to-equity ratio signify in financial terms?

<p>Financial leverage (A)</p> Signup and view all the answers

What is the real interest rate given a nominal interest rate of 7% and an inflation rate of 3%?

<p>4% (A)</p> Signup and view all the answers

If you want to accumulate $50,000 in 15 years with 4% annual interest, how much should you invest today?

<p>$30,834.57 (B)</p> Signup and view all the answers

What does the term 'amortization' refer to?

<p>Spreading loan payments over time (C)</p> Signup and view all the answers

If the annual depreciation of an asset worth $20,000 is $4,000, what is its value after 3 years?

<p>$12,000 (B)</p> Signup and view all the answers

How much will you have after saving $200 monthly at an annual interest rate of 6% for 5 years?

<p>$14,774.38 (D)</p> Signup and view all the answers

What determines the yield to maturity of a bond?

<p>All of the above (D)</p> Signup and view all the answers

What is the current price of a bond with a $1,000 face value, $50 annual coupon, and a yield to maturity of 5% maturing in 10 years?

<p>$1,081.11 (D)</p> Signup and view all the answers

Flashcards

Future Value (FV) of an investment

The total amount you will have after investing a principal amount for a specific time period with compound interest. It is calculated by adding the initial principal amount to the accumulated interest.

Compound Interest

The interest earned on an investment that is calculated on both the principal and any accrued interest. Compounding means that interest is earned on the interest that was previously earned.

Present Value (PV) of a future sum of money

The process of determining the present value of a future sum of money. It is done by discounting the future value by a discount rate, which reflects the time value of money.

Annuity

A stream of equal payments made at regular intervals over a specified period of time. Each payment earns interest, which is added to the principal.

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Effective Annual Rate (EAR)

The effective annual rate (EAR) is the actual annual rate of return on an investment that takes into account the effect of compounding. It is usually higher than the nominal interest rate.

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Simple interest

The interest calculated only on the initial principal amount. There is no compounding of interest.

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Discount Rate

The rate of return that is used to discount future cash flows to their present value. It reflects the time value of money and risk.

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Future Value (FV) of an annuity

The process of determining the future value of a series of equal payments made at regular intervals. It is calculated by compounding the interest earned on each payment.

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Sinking fund

A financial tool used to accumulate funds over time, ensuring the availability of money for a predefined future expense, such as debt repayment or asset replacement. It involves making regular contributions to a dedicated account.

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Liquidity

A financial measure that quantifies the speed and ease with which an asset can be transformed into cash without experiencing a significant loss of value. It signifies an asset's flexibility in being instantly available for transactions.

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Future value of an ordinary annuity formula

A formula used to determine the future value of a series of equal payments made at regular intervals over a certain period, called an annuity. It considers the impact of compound interest on those payments.

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Future Value (FV)

The total amount accumulated at the end of an investment period, considering interest earned.

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Ordinary Annuity

An annuity where payments are made at the end of each period. Imagine the payments coming at the END of each month.

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Principal (P)

The amount of money borrowed or lent that represents the initial principal amount.

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Interest Rate (r)

The interest rate charged per period, typically expressed as an annual percentage rate (APR).

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Number of Periods (n)

The total number of periods over which payments are made, usually expressed in years or months.

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Loan Payment Formula

A formula used to calculate the regular payment amount required to repay a loan over a specific period.

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Rule of 72

A rule of thumb used to quickly estimate the doubling time of an investment, based on its fixed annual interest rate.

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Bond

A financial instrument issued by a corporation or government entity that represents a loan to the issuer, promising to pay regular interest payments and repay the principal at maturity.

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Coupon

The annual interest payment made by a bond, typically expressed as a percentage of the face value.

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Yield to Maturity

The annual rate of return an investor expects to receive from a bond if they hold it until maturity.

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Debt-to-Equity Ratio

A rule of thumb which states that debt-to-equity ratio measures a company’s financial leverage.

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Study Notes

Compound Interest Calculations

  • Formula: A = P(1 + r)t (where A = future value, P = principal, r = interest rate, t = time)
  • Example: Investing $1,000 at 5% annual interest compounded annually for 3 years yields $1,157.63.

Effective Annual Rate (EAR)

  • Formula: EAR = (1 + r/n)n - 1 (where r = nominal rate, n = number of compounding periods per year)
  • Example: A nominal rate of 6% compounded monthly has an EAR of 6.17%.

Simple Interest

  • Formula: I = P × r × t (where I = interest, P = principal, r = interest rate, t = time)
  • Example: A $5,000 loan at 8% simple interest for 2 years results in a total amount owed of $5,800.

Present Value

  • Formula: PV = FV / (1 + r)t (where PV = present value, FV = future value, r = discount rate, t = time)
  • Example: The present value of $10,000 received in 5 years, discounted at 7% annually, is $7,129.86.
  • Key takeaway: The present value is always less than the future value due to the time value of money.

Annuities

  • Characteristics: Equal payments at fixed intervals over a specified period.
  • Not a characteristic: Unlimited term.
  • Example: 10-year ordinary annuity with annual $1,000 payments at 5% results in a future value of $13,207.57.
  • Annuity Due: Payments occur at the beginning of each period. Present value is higher than the ordinary annuity for the same period and rate.

Loan Payments

  • Formula: PMT = P × (r / (1 - (1 + r)-n) (where PMT = monthly payment, P = principal, r = monthly interest rate, n = number of payments)
  • Example: A $20,000 car loan at 6% annual interest over 5 years requires a monthly payment of $386.66.

Rule of 72

  • Purpose: Estimating the doubling time of an investment.
  • Formula: Doubling Time = 72 / Interest Rate

Continuous Compounding

  • Formula: FV = PV × ert (where FV = future value, PV = present value, r = interest rate, t = time, e = exponential base).

Bond Pricing

  • Formula: P = ∑t=1T C / (1 + r)t + F / (1 + r)T (where P = bond price, C = coupon payment, r = yield to maturity, F = face value, T = time to maturity)
  • Example: $1,000 face value bond paying $50 annually with a yield to maturity of 5% matures in 10 years has a price of $1,081.11.

Financial Statement Concepts

  • Equity: Total assets minus total liabilities.
  • Example: A company with $500,000 in assets and $300,000 in liabilities has $200,000 in equity.
  • Debt-to-Equity Ratio: Measures financial leverage (proportion of debt to equity).
  • Liquidity: Ability to convert assets to cash quickly.

Interest Rate Calculations

  • Real Interest Rate: Nominal interest rate minus inflation rate.
  • Example: Nominal rate of 7% with 3% inflation gives a real rate of 4%.

Depreciation

  • Effect: Reduces asset value over time.
  • Example: An asset worth $20,000 depreciating $4,000 annually is worth $12,000 after 3 years.

Sinking Fund

  • Purpose: Savings for a future expense, often to pay off debt.

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Description

Test your understanding of essential finance concepts such as compound interest, effective annual rate, simple interest, and present value. This quiz will help reinforce your knowledge of financial formulas and applications in real-world scenarios.

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