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. (B)</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) (D)</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. (B)</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. (A)</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. (A)</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. (D)</p> Signup and view all the answers

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

<p>Loan repayments (D)</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 (C)</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 (C)</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 (B)</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 (A)</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 (D)</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 (C)</p> Signup and view all the answers

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

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

What is the formula for simple interest?

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

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

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

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

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

What is the formula for the outstanding loan balance?

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

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

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

What is the formula for compound interest?

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

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

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

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

<p>I = T - P (A)</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 (B)</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 (D)</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 (C)</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 (A)</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 (A)</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% (D)</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 (B)</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 (D)</p> Signup and view all the answers

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