Time value of money - an introduction to financial mathematics

Question 1

describe the time value of money, and why a dollar today is worth more than a dollar tomorrow

Answer 1

If we receive $1 today we can invest it, earn interest and end up with more than $1 at any time in the future.

Question 2

how to calculate future value or present value of a single cash flow?

Answer 2

using simple or compound interest calculations

Question 3

simple interest calculation

compound interest calculation

Answer 3

Simple interest

Future Value = Principal + interest

= PV (1 + r_sn)

Compound interest

Future Value = PV (1 + r)ⁿ

Question 4

Future Value of Multiple Cash Flows

Answer 4

–The first deposit ($100) will have been in the bank for exactly two years;
–The second deposit ($200) will have been in the bank for exactly one year; and,
–The third deposit ($500) will be deposited in the bank immediately before the time at which we wish calculate the total value of the deposits.

Question 5

A finite number of cash flows that are equal in value and are evenly spaced are called

Answer 5

annuities

Question 6

what are the 3 types of annuities

Answer 6

–Ordinary Annuities;
–Annuities Due; and,
Deferred Annuities.

Question 7

what is an ordinary annuity?

Answer 7

cash flow occurs at the end of each period

Question 8

how to calculate future value of an annuity comprising n cash flows of $F immediately following the last cash flow?

Answer 8

compound each cash flow individually or

use the future cash flow of an ordinary annuity formula

Question 9

Answer 9

Question 10

To calculate the present value of an ordinary annuity comprising n cash flows of $F, we use the following equation

Answer 10

Question 11

To calculate the present value of an annuity due comprising n cash flows of $F, we use the following equation:

Answer 11

Question 12

To calculate the present value of a deferred annuity that commences in m periods and comprises n cash flows of $F

Answer 12

Question 13

3 types of perpetuities

Answer 13

–Ordinary Perpetuities;
–Perpetuities Due; and,
–Deferred Perpetuities.

Question 14

The present value of an ordinary perpetuity comprising individual cash flows of $F is calculated as:

Answer 14

Question 15

Answer 15

Question 16

present value of an annuity due comprising individual cash flows of $F

Answer 16

Question 17

The present value of a deferred perpetuity commencing in m periods and comprising individual cash flows of $F is calculated

Answer 17

Question 18

Interest Rates for Time Value of Money Calculations

what is an annual nominal interest rate?

Answer 18

An interest rate where interest is charged more frequently than the time period specified in the interest rate. i.e several compunding periods per annum For example, 12% p.a. compounded monthly is an example of a nominal interest rate

Question 19

Answer 19

Question 20

Answer 20

Question 21

Answer 21

Question 22

Answer 22

Question 23

Convert from annual nominal interest rate to an annual effective interest rate

Answer 23

Question 24

conversion from annual effective interest rate (aka compounded annually) to periodic rate

Answer 24

Question 25

conversion from annual nominal rate to periodic rate

Answer 25

r_p= r_n/ n