Interest Rates Quiz

Questions and Answers

What type of interest is calculated only on the principal amount?

Simple Interest (correct)

Compound Interest

Accrued Interest

Discounted Interest

Which formula calculates the total amount including compound interest?

A = P (1 + r)^t

FV = PV × (1 + r)^t

A = P (1 + r/n)^{nt} (correct)

I = P × r × t

How would you calculate the future value of a single sum?

FV = C × (1 + r)^t

FV = C × r^t

FV = PV × (1 + r)^t (correct)

FV = C × (1 + r/n)^{nt}

What defines an ordinary annuity?

Payments are made at the end of each period Signup and view all the answers

Which formula is used to calculate the present value of an annuity?

PVA = C × (1 - (1 + r)^{-t}) / r Signup and view all the answers

What is the purpose of a discount rate in finance?

To determine the present value of future cash flows Signup and view all the answers

What does the term compounding frequency refer to?

How often interest is applied Signup and view all the answers

When using the formula $PV = \frac{FV}{(1 + r)^t}$, what does 'FV' stand for?

Future Value Signup and view all the answers

In the future value formula for multiple cash flows, what does 'C' represent?

Cash flow per period Signup and view all the answers

Which statement correctly describes compound interest?

It is calculated on both principal and accumulated interest. Signup and view all the answers

Study Notes

Interest Rates

Definition: The percentage at which money earns or costs over time.
Types:
- Simple Interest: Interest calculated only on the principal amount.
  - Formula: ( I = P \times r \times t )
- Compound Interest: Interest calculated on both the principal and previously accumulated interest.
  - Formula: ( A = P \left(1 + \frac{r}{n}\right)^{nt} )
    - ( A ): total amount after time ( t )
    - ( P ): principal amount
    - ( r ): annual interest rate (decimal)
    - ( n ): number of times interest applied per time period

Future Value

Definition: The value of an investment at a specific date in the future, based on an assumed rate of growth.
Formula for Future Value (FV):
- For a single sum: ( FV = PV \times (1 + r)^t )
- For multiple cash flows (ordinary annuity):
  - ( FV = C \times \frac{(1 + r)^t - 1}{r} )
    - ( C ): cash flow per period
    - ( t ): number of periods

Annuity Calculations

Definition: A series of equal payments made at regular intervals.
Types:
- Ordinary Annuity: Payments at the end of each period.
- Annuity Due: Payments at the beginning of each period.
Future Value of Annuity (FVA):
- ( FVA = C \times \frac{(1 + r)^t - 1}{r} )
Present Value of Annuity (PVA):
- ( PVA = C \times \frac{1 - (1 + r)^{-t}}{r} )

Present Value

Definition: The current worth of a future sum of money or stream of cash flows given a specified rate of return.
Present Value Formula (PV):
- For single sum: ( PV = \frac{FV}{(1 + r)^t} )
- For multiple cash flows (annuity):
  - ( PV = C \times \frac{1 - (1 + r)^{-t}}{r} )

Key Concepts

Discount Rate: The interest rate used to determine the present value of future cash flows.
Compounding Frequency: Refers to how often interest is applied (e.g., annually, semi-annually, quarterly).
Time Value of Money: The principle that money available today is worth more than the same amount in the future due to its potential earning capacity.

Interest Rates

Represents the cost of borrowing money or the return on investment.
Simple Interest is calculated only on the principal amount using the formula ( I = P \times r \times t ).
Compound Interest calculates interest on both the principal and previously accumulated interest, with the formula ( A = P \left(1 + \frac{r}{n}\right)^{nt} ), where:
- ( A ): total amount after time ( t )
- ( P ): principal amount
- ( r ): annual interest rate (as a decimal)
- ( n ): frequency of interest application per time period

Future Value

Represents what an investment will be worth at a future date based on a specific growth rate.
Future Value (FV) for a single sum is calculated using ( FV = PV \times (1 + r)^t ).
For a series of cash flows (ordinary annuity), Future Value is calculated as ( FV = C \times \frac{(1 + r)^t - 1}{r} ), where:
- ( C ): cash flow per period
- ( t ): total number of periods

Annuity Calculations

Defined as series of equal payments made at regular intervals.
Ordinary Annuity involves payments made at the end of each period, while Annuity Due involves payments at the beginning.
Future Value of Annuity (FVA) is calculated using ( FVA = C \times \frac{(1 + r)^t - 1}{r} ).
Present Value of Annuity (PVA) can be determined with ( PVA = C \times \frac{1 - (1 + r)^{-t}}{r} ).

Present Value

Represents the current value of a future sum of money or cash flows based on a specified rate of return.
Present Value (PV) for a single future sum is calculated via ( PV = \frac{FV}{(1 + r)^t} ).
For a stream of cash flows (annuity), Present Value is computed as ( PV = C \times \frac{1 - (1 + r)^{-t}}{r} ).

Key Concepts

Discount Rate: The interest rate applied to determine the present value of future amounts; it reflects opportunity cost.
Compounding Frequency: Describes how often interest is applied, with common intervals including annually, semi-annually, and quarterly.
Time Value of Money: A fundamental principle stating that current money has greater potential value than the same amount in the future due to its earning capacity.