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?

It indicates how quickly an asset can be converted to cash. Signup and view all the answers

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

The number of payment periods 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?

$1,157.63 Signup and view all the answers

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

EAR = (1 + r/n)^n - 1 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?

$5,800 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?

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

Which of the following statements about annuities is false?

Annuities can have unlimited terms. 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?

$13,207.57 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?

Interest = Principal x Rate x Time Signup and view all the answers

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

The actual rate of interest earned after compounding is taken into account. 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?

$13,207.57 Signup and view all the answers

What formula is used to calculate monthly loan payments?

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

How is the Rule of 72 applied in finance?

To estimate how long it takes for an investment to double Signup and view all the answers

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

FV = PV * e^(rt) 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?

$200,000 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?

$9,649.46 Signup and view all the answers

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

Financial leverage 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%?

4% 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?

$30,834.57 Signup and view all the answers

What does the term 'amortization' refer to?

Spreading loan payments over time 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?

$12,000 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?

$14,774.38 Signup and view all the answers

What determines the yield to maturity of a bond?

All of the above 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?

$1,081.11 Signup and view all the answers

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 × e^rt (where FV = future value, PV = present value, r = interest rate, t = time, e = exponential base).

Bond Pricing

Formula: P = ∑_t=1^T 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.