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 (B)</p>
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In the formula for Effective Annual Rate (EAR), what does 'm' represent?

<p>Number of compounding periods per year (A)</p>
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What does the term 'A' signify in the Simple Interest formula?

<p>Accumulated amount (C)</p>
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What representation does the variable 'x' have in the Present Value of Annuities formula?

<p>Monthly payment amount (B)</p>
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How would you express the formula for Simple Depreciation?

<p>A = P(1 - in) (C)</p>
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What does the formula for Outstanding Loan Balance help to calculate?

<p>Remaining loan balance (A)</p>
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When calculating the Present Value of Annuities, how do you find the payment amount 'x'?

<p>x = P * i / [1 - (1 + i)^{-n}] (B)</p>
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What is the primary purpose of a Future Value Annuity (FVA)?

<p>To accumulate a sum of money in the future (B)</p>
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Which formula calculates the future value of an annuity?

<p>$FV = P \frac{(1 + i)^{n} - 1}{i}$ (A)</p>
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In the context of Present Value Annuities (PVA), what does the variable 'P' represent?

<p>Payment amount per period (D)</p>
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What does the formula for Present Value of an annuity calculate?

<p>The amount necessary to achieve fixed future payments (B)</p>
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What is the role of compound interest in Future Value Annuities?

<p>It is applied to the accumulating amount over the investment period (C)</p>
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What does the variable $A$ represent in the simple interest formula?

<p>Accumulated amount (D)</p>
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Which formula is used to calculate the period $n$ in a compound interest scenario?

<p>$n = rac{ ext{log}(A) - ext{log}(P)}{ ext{log}(1 + i)}$ (C)</p>
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What does the variable 'i' represent in the annuity formulas?

<p>Interest rate per period (C)</p>
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How does a Present Value Annuity (PVA) typically affect borrowers?

<p>It spreads repayment over a series of regular payments (B)</p>
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What type of interest is calculated solely on the principal sum without considering previous interest?

<p>Simple interest (D)</p>
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Which of the following describes the characteristics of Future Value Annuities?

<p>They accumulate funds through regular payments with compound interest. (D)</p>
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When calculating compound depreciation, which formula would you use?

<p>$A = P(1 - i)^n$ (B)</p>
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Which of the following describes an annuity?

<p>A series of equal payments made at regular intervals (D)</p>
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What does the effective interest rate account for that the nominal interest rate does not?

<p>Compounding frequency (A)</p>
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In the context of financial mathematics, what does $P$ typically represent?

<p>Initial investment or principal amount (C)</p>
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How does compound interest differ from simple interest?

<p>It compounds interest on previously earned interest. (B)</p>
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What is the main objective of a Present Value Annuity (PVA)?

<p>To make regular loan repayments (C)</p>
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How does a Future Value Annuity (FVA) primarily accumulate value?

<p>By making regular deposits that earn compound interest (C)</p>
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In the formula for Future Value of an Annuity, what does the variable 'n' represent?

<p>Total number of payments made (D)</p>
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What does the Future Value formula for annuities calculate?

<p>The total value of the investment after all payments (D)</p>
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Which of the following statements is true about Present Value Annuities?

<p>They are used to determine the current worth of future payments. (D)</p>
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What type of interest is applied in a Future Value Annuity?

<p>Compound interest on the accumulating amount (A)</p>
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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 (B)</p>
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What is the primary distinction between simple interest and compound interest?

<p>Compound interest includes interest earned on previous periods. (B)</p>
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Which formula would correctly solve for the number of periods $n$ in a compound interest context?

<p>$n = rac{ ext{log} rac{A}{P}}{ ext{log} (1 + i)}$ (D)</p>
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Which factor is essential when calculating the future value of an annuity?

<p>The interest rate per period applicable to deposits (B)</p>
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What does the term 'annuity' specifically refer to in finance?

<p>A series of equal payments made at regular intervals. (C)</p>
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How is simple depreciation computed over a specific period?

<p>$A = P(1 - in)$ (A)</p>
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Which of the following accurately defines nominal and effective interest rates?

<p>Effective rates reflect the true cost of borrowing over time. (B)</p>
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What is the result of applying the formula for compound depreciation?

<p>The value of assets reduces cumulatively each period. (C)</p>
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What is typically indicated by the variable $i$ in the financial formulas provided?

<p>The interest or depreciation rate per period. (C)</p>
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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. (D)</p>
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What is the formula used to calculate the effective annual rate (EAR)?

<p>$ ext{EAR} = (1 + rac{i_{ ext{nominal}}}{m})^m - 1$ (B)</p>
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Which formula would you use to determine the payment amount 'x' for Future Value Annuities?

<p>$x = rac{F imes i}{(1 + i)^n - 1}$ (D)</p>
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How is total interest paid calculated?

<p>$I = T - P$ (A)</p>
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In the context of the Present Value of an Annuity, what does 'n' represent?

<p>The total number of payments (A)</p>
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Which formula describes the calculation for outstanding loan balance?

<p>$P_{ ext{balance}} = x rac{1 - (1 + i)^{-n}}{i}$ (A)</p>
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What does the formula for compound depreciation look like?

<p>$A = P(1 - i)^n$ (D)</p>
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How do you calculate the time period 'n' using compound interest?

<p>$n = rac{ ext{log}( rac{A}{P})}{ ext{log}(1 + i)}$ (C)</p>
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In the calculation of future value of a series of payments, what does 'F' represent?

<p>Future value of the annuity (A)</p>
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Which calculation method is used to find the present value of an annuity?

<p>$P = x rac{1 - (1 + i)^{-n}}{i}$ (A)</p>
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When calculating compound interest, which mathematical operation is essential for determining the time period $n$?

<p>Logarithmic function (A)</p>
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In the context of depreciation, how does compound depreciation differ from simple depreciation?

<p>It accounts for the asset's reduced value each period. (D)</p>
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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. (C)</p>
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Which formula correctly computes the accumulated amount for simple interest?

<p>$A = P(1 + in)$ (D)</p>
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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. (D)</p>
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Which of the following statements best describes an annuity in financial terms?

<p>A sequence of payments or receipts made at regular intervals. (B)</p>
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What does the variable $n$ represent in the formula for compound interest?

<p>The number of compounding periods (C)</p>
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Which description best fits the formula for compound interest?

<p>Accumulates value based on both principal and prior interest. (A)</p>
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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. (A)</p>
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Which function best characterizes the relationship between nominal and effective interest rates?

<p>Effective rates depend on the frequency of compounding during the year. (D)</p>
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In which scenario would the Outstanding Loan Balance formula be most accurately applied?

<p>To calculate the remaining balance when several payments remain. (B)</p>
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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. (A)</p>
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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. (D)</p>
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What distinguishes compound depreciation from simple depreciation in financial calculations?

<p>Compound applies the depreciation rate to the remaining value each period. (D)</p>
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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. (B)</p>
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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. (D)</p>
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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. (A)</p>
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Which method is primarily used to determine the future value of an annuity?

<p>Applying compound interest formulas (C)</p>
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What is the effect of compound interest on a Future Value Annuity?

<p>It significantly increases the total amount accumulated over time (C)</p>
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Which element is NOT necessary when calculating the Present Value of an Annuity?

<p>Future value of the annuity (C)</p>
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How does the Present Value Annuity formula influence loan repayment strategies?

<p>By establishing the present worth of future payment obligations (C)</p>
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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 (B)</p>
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Which component of the annuity formulas directly influences how quickly investment values will grow?

<p>Interest rate per period (B)</p>
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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 (D)</p>
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Which statement correctly reflects the purpose of Future Value Annuities?

<p>To accumulate a predetermined sum through ongoing contributions (A)</p>
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