Time Value of Money
Future value factors formula
(1+i)^n
Present value factors formula
1/ [(1+i)^n]
FV of an ordinary annuity formula
FV of an ordinary annuity= payment x FV annuity factor
FV of an annuity formula
FV of annuity= payment x future value annuity factor
As the compounding frequency increases, what happened to the present value (opposite of FV)
It decreases due to more frequent compounding (more $ earned on interest=less upfront $
When there's a single payment
Lump sum
When interest is compounded in any way other than annually, you blank, to the interest rate and time period
Make adjustments
To find the future value of an annuity due by table factor
Multiply the ordinary annuity factor by (1+i)
To find the present value of an annuity due table facotr
Multiply the ordinary annuity factor by (1+i)
The FV and PV of annuities are blank
Not reciprocal and can't be used interchangeably
Need to know these 2 variables to determine the table factors
Number of periods (n) and interest rate (i)
Necessary adjustments to i and n
i/# of compounding periods per year n x #of compounds per year
Series of equal payments (paid or received) with same time interval between them
Annuity
Annuity with payments at the beginning of each period
Annuity due
Earns interest on both the principal as well as all previously earned interest
Compound interest
Time value of money=
Compound interest
The frequency with which interest is added to the principal
Compounding
Figuring out how much a future amount is worth today is called blank
Discounting
1. Future value of a lump sum 2. PV of a lump sum 3. FV of an annuity 4. PV of an annuity
Four time value of money cases
In the blank of a lump sum case, we know the value of some amount today and want to know the value at some point in the future
Future value
Wants to have=
Future value
Future value= PV x FV factor i,n
Future value of a lump sum formula
want to know the value of a series of equal cash flows at the beginning of a period in the future
Future value of an annuity due case
we want to know the value of a series of equal cash flows at the end of each period in the future
Future value of an ordinary annuity
As the compounding frequency increases, what happens to the future value
Increases because more frequent compounding= more interest earned on interest
Annuity with payments at the end of each period
Ordinary annuity
The blank in the FV of an annuity formula represents each individual payment
Payment
In the blank case, we know the value of some future amount and want to know today's value
Present value of a lump sum
How much is a series of future payments at the beginning of each period worth today
Present value of an annuity due
Want to know the value today of a series of equal payments to be made/received in the future
Present value of an annuity due case
Want to know the value today of a series of equal payments to be made/received in the future
Present value of an ordinary annuity case
Present value of an ordinary annuity formula
Present value of an ordinary annuity= payment x PV annuity factor
Present value of a lump sum formula
Present value= future value x present value factor
It's always easiest to compare different alternatives using
Present values (value of options in today's dollars)
The pv of a lump sum and the fv of a lump sum are blank
Reciprocals (opposites) and can be used interchangeably
PxRxT Earn interest on the principal invested
Simple interest
In each of the 4 time value of money cases, you will need to use the
Table of factors
When compounding frequency increases
The FV increases
Measurement and recording of liabilities are based on the concept of
Time value of money
