Gr12 Mathematics: Ch 3.2 Annuities

What is the primary purpose of a Future Value Annuity?

To accumulate a sum of money in the future by making regular deposits. (correct)

To calculate the present value of an annuity.

To manage a mortgage bond.

To pay off a loan or debt over time with regular payments.

Which type of annuity is commonly used for loan repayments and mortgage bonds?

Compound Interest Annuity

Future Value Annuity

Present Value Annuity (correct)

Simple Interest Annuity

What is the formula to calculate the Future Value of an Annuity?

FV = P * (1 - (1 + i)^-n) / i

FV = P * ((1 + i)^n - 1) / i (correct)

FV = P * (1 + i)^n

FV = P * i^n

What does the variable 'n' represent in the formulas for Future Value and Present Value of an Annuity?

Number of periods Signup and view all the answers

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

Compound interest Signup and view all the answers

What is the purpose of calculating the Present Value of an Annuity?

To determine the initial amount required to achieve a series of future payments Signup and view all the answers

What is the formula to calculate the Present Value of an Annuity?

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

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

The purpose of the annuity Signup and view all the answers

What is the key concept necessary to understand when managing annuities?

The time value of money Signup and view all the answers

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

It increases the amount Signup and view all the answers

What is the purpose of calculating the Future Value of an Annuity?

To determine the total value of the investment after all payments have been made Signup and view all the answers

What is the relationship between the interest rate and the number of periods in the formula for Present Value of an Annuity?

They are inversely proportional Signup and view all the answers

What is the primary difference between a Future Value Annuity and a Present Value Annuity in terms of their purpose?

One is used for investment while the other is used for loan repayment Signup and view all the answers

What is the effect of an increase in the interest rate on the Future Value of an Annuity?

It increases the Future Value Signup and view all the answers

What is the purpose of using an annuity in a retirement fund?

To accumulate a sum of money in the future Signup and view all the answers

What is the effect of an increase in the number of periods on the Present Value of an Annuity?

It decreases the Present Value Signup and view all the answers

If an individual deposits $1,000 at the end of each year for 5 years into a savings account that earns an annual interest rate of 5%, what will be the future value of the annuity?

$5,775.08 Signup and view all the answers

A company takes a loan of $100,000 to finance a new project. If the loan is to be repaid in equal annual installments over 10 years at an annual interest rate of 6%, what will be the annual payment?

$12,147.89 Signup and view all the answers

Which of the following statements is true about the relationship between the interest rate and the number of periods in the formula for Future Value of an Annuity?

As the interest rate increases, the future value of the annuity increases. Signup and view all the answers

What will be the present value of an annuity that provides annual payments of $5,000 for 8 years at an annual interest rate of 4%?

$33,411.89 Signup and view all the answers

Which of the following statements is true about the effect of compound interest on the accumulating amount in a Future Value Annuity?

Compound interest increases the accumulating amount. Signup and view all the answers

If the interest rate increases in a Present Value Annuity, what will be the effect on the present value?

The present value will decrease. Signup and view all the answers

What will be the future value of an annuity that provides annual deposits of $2,000 for 12 years at an annual interest rate of 7%?

$45,113.51 Signup and view all the answers

Which of the following statements is true about the relationship between the interest rate and the number of periods in the formula for Present Value of an Annuity?

As the interest rate increases, the present value of the annuity decreases. Signup and view all the answers