Gr12 Mathematics: Ch 3 Sum Finance
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Questions and Answers

What is the formula to calculate the accumulated amount in simple interest?

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

    • What is the difference between simple interest and compound interest?

  • Compound interest is calculated on the initial principal, while simple interest is calculated on the principal and interest from previous periods.
  • Simple interest is used for short-term investments, while compound interest is used for long-term investments.
  • Simple interest is calculated on the initial principal, while compound interest is calculated on the principal and interest from previous periods. (correct)
  • Simple interest is used for long-term investments, while compound interest is used for short-term investments.

    • What is the formula to calculate the value after depreciation using compound depreciation?

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

    • What is the relationship between nominal and effective interest rates?

    <p>Nominal interest rate is the stated interest rate, while effective interest rate is the actual rate received or paid.</p> Signup and view all the answers

    What is the formula to solve for the time period n in compound interest calculations?

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

    What is an annuity?

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

    What is the purpose of using logarithms in compound interest calculations?

    <p>To solve for the time period n.</p> Signup and view all the answers

    What is the difference between simple depreciation and compound depreciation?

    <p>Simple depreciation does not consider the reduced value in each period, while compound depreciation does.</p> Signup and view all the answers

    What is the main purpose of a Future Value Annuity?

    <p>To accumulate a sum of money in the future by making regular deposits.</p> Signup and view all the answers

    Which of the following is a common use of a Present Value Annuity?

    <p>Loan repayments</p> Signup and view all the answers

    What type of interest is applied to the accumulating amount in a Future Value Annuity?

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

    What does the formula FV = P [(1 + i)^n - 1] / i calculate?

    <p>The future value of an annuity</p> Signup and view all the answers

    What is the variable 'n' in the formulas for the future value and present value of an annuity?

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

    What is the main difference between a Future Value Annuity and a Present Value Annuity?

    <p>The direction of the cash flow</p> Signup and view all the answers

    What is the formula for the present value of an annuity?

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

    What is the purpose of calculating the present value of an annuity?

    <p>To determine the installment amount for a loan repayment</p> Signup and view all the answers

    What is the formula for the present value of an annuity?

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

    What is the formula for simple interest?

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

    What is the formula for the effective annual rate (EAR)?

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

    What is the formula for the future value of an annuity?

    <p>$F = x \left[\frac{(1 + i)^n - 1}{i}\right]$</p> Signup and view all the answers

    What is the formula for the outstanding loan balance?

    <p>$P_{balance} = x \left[\frac{1 - (1 + i)^{-n_{remaining}}}{i}\right]$</p> Signup and view all the answers

    What is the formula for calculating the payment amount for a present value annuity?

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

    What is the formula for compound interest?

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

    What is the formula for calculating the period of an investment using compound interest?

    <p>$n = \frac{\log\left(\frac{A}{P}\right)}{\log(1 + i)}$</p> Signup and view all the answers

    What is the formula for the total interest paid on a loan?

    Signup and view all the answers

    What is the purpose of using logarithms in solving for the period of an investment in compound interest calculations?

    <p>To isolate the variable 'n'</p> Signup and view all the answers

    If an asset depreciates by 10% each year, what is the formula to calculate its value after 5 years?

    <p>A = P(1 - 0.1)^5</p> Signup and view all the answers

    A company deposits $1,000 at the end of each year for 10 years into an account that earns an annual interest rate of 8%. What is the accumulated amount after 10 years?

    <p>$23,152.19</p> Signup and view all the answers

    What is the effective annual interest rate if the nominal interest rate is 12%, compounded quarterly?

    <p>12.55%</p> Signup and view all the answers

    If an investment grows from $10,000 to $15,000 in 5 years, what is the compound annual growth rate?

    <p>10%</p> Signup and view all the answers

    What is the formula to calculate the value of an asset after 10 years of depreciation, if the initial value is $100,000 and the annual depreciation rate is 5%?

    <p>A = P(1 - 0.05)^10</p> Signup and view all the answers

    What is the purpose of calculating the present value of an annuity?

    <p>To determine the total amount of money needed to make a series of payments</p> Signup and view all the answers

    If a company deposits $5,000 at the beginning of each year for 8 years into an account that earns an annual interest rate of 6%, what is the accumulated amount after 8 years?

    <p>$43,919.49</p> Signup and view all the answers

    What is the primary goal of a Future Value Annuity?

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

    What is the primary application of the formula FV = P [(1 + i)^n - 1] / i?

    <p>To calculate the future value of an annuity</p> Signup and view all the answers

    What type of interest is applied to the reducing balance of a loan in a Present Value Annuity?

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

    What is the purpose of calculating the present value of an annuity?

    <p>To calculate the initial amount required to achieve a series of future payments</p> Signup and view all the answers

    What is the formula for calculating the present value of an annuity?

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

    What does the variable 'P' represent in the formulas for the future value and present value of an annuity?

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

    What is the main difference between a Future Value Annuity and a Present Value Annuity?

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

    What is the result of calculating the future value of an annuity?

    <p>The total value of the investment after all payments have been made and compounded with interest</p> Signup and view all the answers

    What is the purpose of calculating the present value of an annuity?

    <p>To determine the current value of a series of future cash flows</p> Signup and view all the answers

    If the interest rate per period is 5% and the number of periods is 10, what is the future value of an annuity with a regular payment amount of $1,000?

    <p>$7,378.19</p> Signup and view all the answers

    What is the effective annual rate of an investment with a nominal interest rate of 12% compounded quarterly?

    <p>12.55%</p> Signup and view all the answers

    What is the outstanding loan balance after 5 years of payments on a $50,000 loan with a monthly payment amount of $1,000 and an interest rate of 6% per year?

    <p>$28,500.00</p> Signup and view all the answers

    If the principal amount is $10,000 and the accumulated amount is $12,100 after 5 years, what is the interest rate per period?

    <p>4.20%</p> Signup and view all the answers

    What is the total amount paid on a $20,000 loan with a monthly payment amount of $500 and an interest rate of 8% per year over 4 years?

    <p>$25,600.00</p> Signup and view all the answers

    If the present value of an annuity is $10,000 and the regular payment amount is $1,000, what is the interest rate per period?

    <p>4.75%</p> Signup and view all the answers

    What is the change of base formula for logarithms?

    <p>log_a x = log_b x / log_b a</p> Signup and view all the answers

    If the accumulated amount is $15,000 and the principal amount is $10,000, what is the total interest paid?

    <p>$5,000.00</p> Signup and view all the answers

    What is the future value of a series of payments of $1,000 per period for 10 periods with an interest rate of 4% per period?

    <p>$12,166.53</p> Signup and view all the answers

    What is the relationship between the number of periods and the interest rate in the formula for compound interest?

    <p>The number of periods is exponentially related to the interest rate.</p> Signup and view all the answers

    Which type of interest is applied to the accumulating amount in a Present Value Annuity?

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

    What is the role of logarithms in solving for the period of an investment in compound interest calculations?

    <p>To solve for the number of periods</p> Signup and view all the answers

    If an asset depreciates by 15% each year, what is the formula to calculate its value after 3 years?

    <p>A = P(1 - 0.15)^3</p> Signup and view all the answers

    What is the relationship between the effective annual interest rate and the nominal interest rate compounded m times per year?

    <p>The effective annual interest rate is related to the nominal interest rate by the formula 1 + i = (1 + i_(m)/m)^m</p> Signup and view all the answers

    If a company deposits $2,000 at the end of each year for 7 years into an account that earns an annual interest rate of 7%, what is the formula to calculate the accumulated amount?

    <p>A = 2000((1 + 0.07)^7 - 1) / 0.07</p> Signup and view all the answers

    What is the purpose of calculating the present value of an annuity?

    <p>To evaluate the current worth of a series of future cash flows</p> Signup and view all the answers

    If the accumulated amount is $12,000 and the principal amount is $10,000, what is the interest earned?

    <p>$1,000</p> Signup and view all the answers

    What is the primary reason for using compound interest in Future Value Annuities?

    <p>To calculate the total value of the annuity after a specified period</p> Signup and view all the answers

    A company deposits $2,000 at the end of each quarter into an account that earns an interest rate of 4% per quarter. How much will the company have in the account after 5 years?

    <p>Approximately $41,923</p> Signup and view all the answers

    What is the purpose of calculating the present value of an annuity in a loan repayment scenario?

    <p>To calculate the initial amount required to repay the loan</p> Signup and view all the answers

    If a person deposits $500 at the end of each month into an account that earns an interest rate of 3% per month, what is the total value of the annuity after 10 years?

    <p>Approximately $77,119</p> Signup and view all the answers

    What is the main difference between a Future Value Annuity and a Present Value Annuity?

    <p>The direction of cash flow</p> Signup and view all the answers

    A person borrows $30,000 to purchase a car and agrees to repay the loan with monthly payments of $500 over 5 years. What is the total interest paid on the loan?

    <p>Approximately $6,813</p> Signup and view all the answers

    What is the result of calculating the present value of an annuity?

    <p>The initial amount required to achieve a series of future payments</p> Signup and view all the answers

    A company deposits $1,500 at the beginning of each quarter into an account that earns an interest rate of 5% per quarter. How much will the company have in the account after 7 years?

    <p>Approximately $61,947</p> Signup and view all the answers

    If a company deposits $2,000 at the end of each quarter for 5 years into an account that earns a quarterly interest rate of 2%, what is the accumulated amount after 5 years?

    <p>$50,102.11</p> Signup and view all the answers

    If an asset depreciates by 8% each year, what is the formula to calculate its value after 7 years?

    <p>P(1 - 0.08)^7</p> Signup and view all the answers

    What is the effective annual rate if the nominal interest rate is 15%, compounded monthly?

    <p>16.06%</p> Signup and view all the answers

    If a $30,000 loan has a monthly payment amount of $500 and an interest rate of 9% per year, what is the total interest paid over 6 years?

    <p>$14,179.21</p> Signup and view all the answers

    What is the formula to calculate the change of base for logarithms?

    <p>log_a x = log_b x / log_b a</p> Signup and view all the answers

    If an investment grows from $5,000 to $7,500 in 3 years, what is the compound annual growth rate?

    <p>11.03%</p> Signup and view all the answers

    What is the outstanding loan balance after 3 years of payments on a $40,000 loan with a monthly payment amount of $800 and an interest rate of 7% per year?

    <p>$23,459.15</p> Signup and view all the answers

    If a company deposits $3,000 at the beginning of each year for 6 years into an account that earns an annual interest rate of 5%, what is the accumulated amount after 6 years?

    <p>$22,219.11</p> Signup and view all the answers

    If the present value of an annuity is $25,000 and the regular payment amount is $2,000, what is the interest rate per period?

    <p>8.50%</p> Signup and view all the answers

    What is the total amount paid on a $25,000 loan with a monthly payment amount of $600 and an interest rate of 9% per year over 5 years?

    <p>$36,489.15</p> Signup and view all the answers

    What is the purpose of calculating the present value of an annuity?

    <p>To determine the current value of a series of future cash flows</p> Signup and view all the answers

    What is the formula to calculate the total interest paid on a loan?

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

    What is the result of calculating the future value of an annuity?

    <p>The accumulated value of a series of payments</p> Signup and view all the answers

    What is the main difference between a Future Value Annuity and a Present Value Annuity?

    <p>The direction of cash flows</p> Signup and view all the answers

    What is the purpose of using logarithms in compound interest calculations?

    <p>To calculate the number of periods in an investment</p> Signup and view all the answers

    What does the variable 'x' represent in the formulas for the future value and present value of an annuity?

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

    What is the formula to calculate the outstanding loan balance?

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

    What is the effective annual rate (EAR) of an investment with a nominal interest rate of 12% compounded quarterly?

    <p>12.55%</p> Signup and view all the answers

    What is the purpose of calculating the future value of an annuity?

    <p>To determine the accumulated value of a series of payments</p> Signup and view all the answers

    What is the change of base formula for logarithms?

    <p>log_a x = log_b x / log_b a</p> Signup and view all the answers

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