Gr12 Mathematics: Ch 3 Sum Finance
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Questions and Answers

What does the variable 'P' represent in the Present Value of an Annuity formula?

  • Present value of the loan or annuity (correct)
  • Interest rate per period
  • Payment amount per period
  • Future value of the annuity

    • Which formula correctly calculates the Future Value of Annuities?

  • F = x [(1 + i)^(n) - 1] (correct)
  • F = x [i/(1 + i)^n - 1]
  • F = x [1 + in]
  • F = x [(1 - (1 + i)^{-n})/i]

    • How is the time period 'n' determined when using compound interest?

  • n = A/P
  • n = P(1 + i)/A
  • n = log(A/P) / log(1 + i) (correct)
  • n = (1 + i)^(A/P)

    • What is the formula for calculating Total Interest Paid on a loan?

    <p>I = T - P</p> Signup and view all the answers

    In the formula for Effective Annual Rate (EAR), what does 'm' represent?

    <p>Number of compounding periods per year</p> Signup and view all the answers

    What does the term 'A' signify in the Simple Interest formula?

    <p>Accumulated amount</p> Signup and view all the answers

    What representation does the variable 'x' have in the Present Value of Annuities formula?

    <p>Monthly payment amount</p> Signup and view all the answers

    How would you express the formula for Simple Depreciation?

    <p>A = P(1 - in)</p> Signup and view all the answers

    What does the formula for Outstanding Loan Balance help to calculate?

    <p>Remaining loan balance</p> Signup and view all the answers

    When calculating the Present Value of Annuities, how do you find the payment amount 'x'?

    <p>x = P * i / [1 - (1 + i)^{-n}]</p> Signup and view all the answers

    What is the primary purpose of a Future Value Annuity (FVA)?

    <p>To accumulate a sum of money in the future</p> Signup and view all the answers

    Which formula calculates the future value of an annuity?

    <p>$FV = P \frac{(1 + i)^{n} - 1}{i}$</p> Signup and view all the answers

    In the context of Present Value Annuities (PVA), what does the variable 'P' represent?

    <p>Payment amount per period</p> Signup and view all the answers

    What does the formula for Present Value of an annuity calculate?

    <p>The amount necessary to achieve fixed future payments</p> Signup and view all the answers

    What is the role of compound interest in Future Value Annuities?

    <p>It is applied to the accumulating amount over the investment period</p> Signup and view all the answers

    What does the variable $A$ represent in the simple interest formula?

    <p>Accumulated amount</p> Signup and view all the answers

    Which formula is used to calculate the period $n$ in a compound interest scenario?

    <p>$n = rac{ ext{log}(A) - ext{log}(P)}{ ext{log}(1 + i)}$</p> Signup and view all the answers

    What does the variable 'i' represent in the annuity formulas?

    <p>Interest rate per period</p> Signup and view all the answers

    How does a Present Value Annuity (PVA) typically affect borrowers?

    <p>It spreads repayment over a series of regular payments</p> Signup and view all the answers

    What type of interest is calculated solely on the principal sum without considering previous interest?

    <p>Simple interest</p> Signup and view all the answers

    Which of the following describes the characteristics of Future Value Annuities?

    <p>They accumulate funds through regular payments with compound interest.</p> Signup and view all the answers

    When calculating compound depreciation, which formula would you use?

    <p>$A = P(1 - i)^n$</p> Signup and view all the answers

    Which of the following describes an annuity?

    <p>A series of equal payments made at regular intervals</p> Signup and view all the answers

    What does the effective interest rate account for that the nominal interest rate does not?

    <p>Compounding frequency</p> Signup and view all the answers

    In the context of financial mathematics, what does $P$ typically represent?

    <p>Initial investment or principal amount</p> Signup and view all the answers

    How does compound interest differ from simple interest?

    <p>It compounds interest on previously earned interest.</p> Signup and view all the answers

    What is the main objective of a Present Value Annuity (PVA)?

    <p>To make regular loan repayments</p> Signup and view all the answers

    How does a Future Value Annuity (FVA) primarily accumulate value?

    <p>By making regular deposits that earn compound interest</p> Signup and view all the answers

    In the formula for Future Value of an Annuity, what does the variable 'n' represent?

    <p>Total number of payments made</p> Signup and view all the answers

    What does the Future Value formula for annuities calculate?

    <p>The total value of the investment after all payments</p> Signup and view all the answers

    Which of the following statements is true about Present Value Annuities?

    <p>They are used to determine the current worth of future payments.</p> Signup and view all the answers

    What type of interest is applied in a Future Value Annuity?

    <p>Compound interest on the accumulating amount</p> Signup and view all the answers

    The formula for Present Value of an Annuity helps to determine which of the following?

    <p>The current value required to fulfill a series of future payments</p> Signup and view all the answers

    What is the primary distinction between simple interest and compound interest?

    <p>Compound interest includes interest earned on previous periods.</p> Signup and view all the answers

    Which formula would correctly solve for the number of periods $n$ in a compound interest context?

    <p>$n = rac{ ext{log} rac{A}{P}}{ ext{log} (1 + i)}$</p> Signup and view all the answers

    Which factor is essential when calculating the future value of an annuity?

    <p>The interest rate per period applicable to deposits</p> Signup and view all the answers

    What does the term 'annuity' specifically refer to in finance?

    <p>A series of equal payments made at regular intervals.</p> Signup and view all the answers

    How is simple depreciation computed over a specific period?

    <p>$A = P(1 - in)$</p> Signup and view all the answers

    Which of the following accurately defines nominal and effective interest rates?

    <p>Effective rates reflect the true cost of borrowing over time.</p> Signup and view all the answers

    What is the result of applying the formula for compound depreciation?

    <p>The value of assets reduces cumulatively each period.</p> Signup and view all the answers

    What is typically indicated by the variable $i$ in the financial formulas provided?

    <p>The interest or depreciation rate per period.</p> Signup and view all the answers

    Which of the following statements about the future value of an annuity is true?

    <p>It sums up the payments made with interest over time.</p> Signup and view all the answers

    What is the formula used to calculate the effective annual rate (EAR)?

    <p>$ ext{EAR} = (1 + rac{i_{ ext{nominal}}}{m})^m - 1$</p> Signup and view all the answers

    Which formula would you use to determine the payment amount 'x' for Future Value Annuities?

    <p>$x = rac{F imes i}{(1 + i)^n - 1}$</p> Signup and view all the answers

    How is total interest paid calculated?

    <p>$I = T - P$</p> Signup and view all the answers

    In the context of the Present Value of an Annuity, what does 'n' represent?

    <p>The total number of payments</p> Signup and view all the answers

    Which formula describes the calculation for outstanding loan balance?

    <p>$P_{ ext{balance}} = x rac{1 - (1 + i)^{-n}}{i}$</p> Signup and view all the answers

    What does the formula for compound depreciation look like?

    <p>$A = P(1 - i)^n$</p> Signup and view all the answers

    How do you calculate the time period 'n' using compound interest?

    <p>$n = rac{ ext{log}( rac{A}{P})}{ ext{log}(1 + i)}$</p> Signup and view all the answers

    In the calculation of future value of a series of payments, what does 'F' represent?

    <p>Future value of the annuity</p> Signup and view all the answers

    Which calculation method is used to find the present value of an annuity?

    <p>$P = x rac{1 - (1 + i)^{-n}}{i}$</p> Signup and view all the answers

    When calculating compound interest, which mathematical operation is essential for determining the time period $n$?

    <p>Logarithmic function</p> Signup and view all the answers

    In the context of depreciation, how does compound depreciation differ from simple depreciation?

    <p>It accounts for the asset's reduced value each period.</p> Signup and view all the answers

    Which of the following correctly represents the relationship between nominal and effective interest rates?

    <p>Effective interest rate is higher when compounding occurs more frequently.</p> Signup and view all the answers

    Which formula correctly computes the accumulated amount for simple interest?

    <p>$A = P(1 + in)$</p> Signup and view all the answers

    What is the main factor affecting the effective annual interest rate as compared to the nominal rate?

    <p>The frequency of compounding periods in a year.</p> Signup and view all the answers

    Which of the following statements best describes an annuity in financial terms?

    <p>A sequence of payments or receipts made at regular intervals.</p> Signup and view all the answers

    What does the variable $n$ represent in the formula for compound interest?

    <p>The number of compounding periods</p> Signup and view all the answers

    Which description best fits the formula for compound interest?

    <p>Accumulates value based on both principal and prior interest.</p> Signup and view all the answers

    How does the formula for calculating the payment amount 'x' for Future Value Annuities differ from other payment calculations?

    <p>It includes the total future value and interest rate over a period.</p> Signup and view all the answers

    Which function best characterizes the relationship between nominal and effective interest rates?

    <p>Effective rates depend on the frequency of compounding during the year.</p> Signup and view all the answers

    In which scenario would the Outstanding Loan Balance formula be most accurately applied?

    <p>To calculate the remaining balance when several payments remain.</p> Signup and view all the answers

    Which of the following accurately describes the process of calculating the Effective Annual Rate (EAR)?

    <p>It involves applying the nominal rate and compounding it over the year.</p> Signup and view all the answers

    How is the future value of a series of payments notably different from the calculation of simple interest?

    <p>It compounds interest on each contribution made over time.</p> Signup and view all the answers

    What distinguishes compound depreciation from simple depreciation in financial calculations?

    <p>Compound applies the depreciation rate to the remaining value each period.</p> Signup and view all the answers

    In loan analysis, how does total interest paid relate to principal and total amount paid?

    <p>It signifies the difference between the principal and total amount paid.</p> Signup and view all the answers

    What is a critical factor to consider when calculating the present value of an annuity?

    <p>The number of annuity payments must be fixed and known.</p> Signup and view all the answers

    Which step is essential in transitioning from logarithms of one base to another in financial mathematics?

    <p>Dividing the logarithm of the target value by the logarithm of the new base.</p> Signup and view all the answers

    Which method is primarily used to determine the future value of an annuity?

    <p>Applying compound interest formulas</p> Signup and view all the answers

    What is the effect of compound interest on a Future Value Annuity?

    <p>It significantly increases the total amount accumulated over time</p> Signup and view all the answers

    Which element is NOT necessary when calculating the Present Value of an Annuity?

    <p>Future value of the annuity</p> Signup and view all the answers

    How does the Present Value Annuity formula influence loan repayment strategies?

    <p>By establishing the present worth of future payment obligations</p> Signup and view all the answers

    What is a fundamental difference between Future Value Annuities and Present Value Annuities?

    <p>Future Value Annuities aim to grow savings while Present Value Annuities focus on repayment</p> Signup and view all the answers

    Which component of the annuity formulas directly influences how quickly investment values will grow?

    <p>Interest rate per period</p> Signup and view all the answers

    In what scenario would one primarily use the Present Value of an Annuity formula?

    <p>When calculating how much to borrow based on future payment terms</p> Signup and view all the answers

    Which statement correctly reflects the purpose of Future Value Annuities?

    <p>To accumulate a predetermined sum through ongoing contributions</p> Signup and view all the answers

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