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Interest and Discount Factors

Description: This quiz covers the fundamental concepts related to interest and discount factors, which play a crucial role in various financial calculations and decision-making processes.
Number of Questions: 14
Created by:
Tags: interest discount factors time value of money financial mathematics
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What is the formula for calculating the future value (FV) of a present value (PV) at a given interest rate (r) for a specified number of periods (n)?

  1. FV = PV * (1 + r)^n

  2. FV = PV * (1 - r)^n

  3. FV = PV * (1 + r/n)^n

  4. FV = PV * (1 - r/n)^n

Show answer
Correct Option: A
Explanation:

The future value (FV) is calculated by multiplying the present value (PV) by the factor (1 + r)^n, where r is the interest rate and n is the number of periods.

What is the formula for calculating the present value (PV) of a future value (FV) at a given interest rate (r) for a specified number of periods (n)?

  1. PV = FV / (1 + r)^n

  2. PV = FV / (1 - r)^n

  3. PV = FV / (1 + r/n)^n

  4. PV = FV / (1 - r/n)^n

Show answer
Correct Option: A
Explanation:

The present value (PV) is calculated by dividing the future value (FV) by the factor (1 + r)^n, where r is the interest rate and n is the number of periods.

What is the relationship between the future value (FV) and the present value (PV) of a cash flow at a given interest rate (r) for a specified number of periods (n)?

  1. FV = PV * (1 + r)^n

  2. FV = PV * (1 - r)^n

  3. FV = PV * (1 + r/n)^n

  4. FV = PV * (1 - r/n)^n

Show answer
Correct Option: A
Explanation:

The future value (FV) is calculated by multiplying the present value (PV) by the factor (1 + r)^n, where r is the interest rate and n is the number of periods.

What is the formula for calculating the discount factor (DF) at a given interest rate (r) for a specified number of periods (n)?

  1. DF = (1 + r)^n

  2. DF = (1 - r)^n

  3. DF = (1 + r/n)^n

  4. DF = (1 - r/n)^n

Show answer
Correct Option:
Explanation:

The discount factor (DF) is calculated by raising the factor (1 + r) to the power of -n, where r is the interest rate and n is the number of periods.

What is the relationship between the discount factor (DF) and the future value (FV) of a cash flow at a given interest rate (r) for a specified number of periods (n)?

  1. FV = DF * PV

  2. FV = DF / PV

  3. FV = PV / DF

  4. FV = DF - PV

Show answer
Correct Option: A
Explanation:

The future value (FV) of a cash flow is calculated by multiplying the present value (PV) by the discount factor (DF).

What is the relationship between the discount factor (DF) and the present value (PV) of a cash flow at a given interest rate (r) for a specified number of periods (n)?

  1. PV = DF * FV

  2. PV = DF / FV

  3. PV = FV / DF

  4. PV = DF - FV

Show answer
Correct Option: A
Explanation:

The present value (PV) of a cash flow is calculated by multiplying the future value (FV) by the discount factor (DF).

In a loan repayment schedule, what is the difference between the interest payment and the principal payment?

  1. Interest payment is the amount paid towards the loan principal, while principal payment is the amount paid towards the interest.

  2. Interest payment is the amount paid towards the interest, while principal payment is the amount paid towards the loan principal.

  3. Interest payment is the amount paid towards the total loan amount, while principal payment is the amount paid towards the remaining loan amount.

  4. Interest payment is the amount paid towards the remaining loan amount, while principal payment is the amount paid towards the total loan amount.

Show answer
Correct Option: B
Explanation:

In a loan repayment schedule, the interest payment is the amount paid towards the interest accrued on the loan, while the principal payment is the amount paid towards reducing the outstanding loan principal.

What is the formula for calculating the effective annual interest rate (EAR) from the nominal annual interest rate (r) and the number of compounding periods (m)?

  1. EAR = (1 + r/m)^m - 1

  2. EAR = (1 - r/m)^m - 1

  3. EAR = (1 + r*m)^m - 1

  4. EAR = (1 - r*m)^m - 1

Show answer
Correct Option: A
Explanation:

The effective annual interest rate (EAR) is calculated using the formula EAR = (1 + r/m)^m - 1, where r is the nominal annual interest rate and m is the number of compounding periods.

What is the relationship between the effective annual interest rate (EAR) and the nominal annual interest rate (r) when the interest is compounded continuously?

  1. EAR = e^r - 1

  2. EAR = e^-r - 1

  3. EAR = (e^r)^m - 1

  4. EAR = (e^-r)^m - 1

Show answer
Correct Option: A
Explanation:

When the interest is compounded continuously, the effective annual interest rate (EAR) is calculated using the formula EAR = e^r - 1, where r is the nominal annual interest rate.

What is the formula for calculating the present value of an annuity (PVA) at a given interest rate (r) for a specified number of periods (n)?

  1. PVA = PMT * [(1 - (1 + r)^-n) / r]

  2. PVA = PMT * [(1 + (1 + r)^-n) / r]

  3. PVA = PMT * [(1 - (1 - r)^-n) / r]

  4. PVA = PMT * [(1 + (1 - r)^-n) / r]

Show answer
Correct Option: A
Explanation:

The present value of an annuity (PVA) is calculated using the formula PVA = PMT * [(1 - (1 + r)^-n) / r], where PMT is the periodic payment, r is the interest rate, and n is the number of periods.

What is the formula for calculating the future value of an annuity (FVA) at a given interest rate (r) for a specified number of periods (n)?

  1. FVA = PMT * [(1 + (1 + r)^n) / r - 1]

  2. FVA = PMT * [(1 - (1 + r)^n) / r - 1]

  3. FVA = PMT * [(1 + (1 - r)^n) / r - 1]

  4. FVA = PMT * [(1 - (1 - r)^n) / r - 1]

Show answer
Correct Option: A
Explanation:

The future value of an annuity (FVA) is calculated using the formula FVA = PMT * [(1 + (1 + r)^n) / r - 1], where PMT is the periodic payment, r is the interest rate, and n is the number of periods.

What is the formula for calculating the present value of a perpetuity (PV perp) at a given interest rate (r)?

  1. PV perp = PMT / r

  2. PV perp = PMT * r

  3. PV perp = PMT * (1 + r)

  4. PV perp = PMT * (1 - r)

Show answer
Correct Option: A
Explanation:

The present value of a perpetuity (PV perp) is calculated using the formula PV perp = PMT / r, where PMT is the periodic payment and r is the interest rate.

What is the formula for calculating the future value of a perpetuity (FV perp) at a given interest rate (r)?

  1. FV perp = PMT / r

  2. FV perp = PMT * r

  3. FV perp = PMT * (1 + r)

  4. FV perp = PMT * (1 - r)

Show answer
Correct Option: A
Explanation:

The future value of a perpetuity (FV perp) is calculated using the formula FV perp = PMT / r, where PMT is the periodic payment and r is the interest rate.

What is the formula for calculating the sinking fund payment (SFP) required to accumulate a future value (FV) at a given interest rate (r) for a specified number of periods (n)?

  1. SFP = FV * r / [(1 + r)^n - 1]

  2. SFP = FV * r / [(1 - r)^n - 1]

  3. SFP = FV * r / [(1 + r/n)^n - 1]

  4. SFP = FV * r / [(1 - r/n)^n - 1]

Show answer
Correct Option: A
Explanation:

The sinking fund payment (SFP) is calculated using the formula SFP = FV * r / [(1 + r)^n - 1], where FV is the future value, r is the interest rate, and n is the number of periods.

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