Chapter 3: Understanding and Appreciating the Time Value of Money
Annual Interest Rate (i)
Rate charged or paid for use of money on an annual basis
Rule of 72
States that you can determine how many years it will take for a sum to double by dividing the annual growth rate into 72 - this is an approximation
Reinvesting
Taking money that you have earned on an investment and plowing it back into that investment
Compounded Annually
The interest received at the end of each year added to the original investment - at the end of the 2nd year, interest is earned on this new sum
Compound Interest with Non-Annual Periods
- quarterly, daily, continuous - you earn money faster - calculated with a financial calculator
Compounding and the Power of Time and Interest Rate in Compounding
- together, time and interest rate determine how large an investment grows - you can increase the future value by increasing the interest rate or the # of periods that your money is compounded
Time Value of Money
A dollar received today is worth more than a dollar received in the future (therefore, you cannot compare amounts in different time periods without adjusting their values)
Annuity
A serious of equal annual dollar payments coming at the end of each year for a specified number of years - because annuities occur frequently in finance, for example, as bond interest payments and mortgage payments, they receive special treatment - a compound annuity involves depositing or investing an equal sum of money at the end of each year for a certain number of. Years and allowing it to grow
Perpetuity
Annuity that continues forever
Present Value (PV)
Current value in today's dollars of a future sum of money
Future-Value Interest Factor of an Annuity
Multiplier used to determine the future value of an annuity
Present Value Interest Factor of an Annuity
Multiplier used to determine the present value of an annuity
Compound Interest
Effect of earning interest on interest, resulting from the reinvestment of interest paid on an investment's principal - if you take the interest you earn on an investment and reinvest it, you start earning interest on the principal and the reinvested interest (the amount of interest you earn compounds [grows])
Time Value of Money Formula
FV = PV (1 + i)^n FV = Future Value PV = Present Value i = Annual Interest Rate N = # periods/years
Future Value of Annuity Formula
FVn = PMT X Future Value Interest Factor of an Annuity FVn = Future Value of an Annuity PMT = Annual Payment
Principal
Face value of deposit or debt instrument
Present Value Formula
PV = FV (1 / [1+i]^n)
Present Value of an Annuity Formula
PV = PMT X Present Value Interest Factor of an Annuity
Discount Rate
Interest rate used to bring future dollars back to present
Compound Annuity
Investment that involves depositing an equal sum of money at the end of each year for a certain number of years and allowing it to grow
Future-Value Interest Factor [(1+i)^n]
Used as a multiplier to calculate an amount's future value
Present-Value Interest Factor (1 / [1+i]^n)
Used as multiplier to calculate an amount's present value
Future Value (FV)
Value of an investment at some future point in time
Amortized Loan
loan paid off in equal installments
