Zarestky
Math 141
Chapter 5 Notes
5.1 Compound Interest
Simple interest is earned/paid on the original principal only.
• Formula: I = P ! r ! t
o I represents the total amount of interest.
o P represents the initial investment or principal.
o r represents the annual interest rate in decimal form.
o t represents time (usually in years).
• Total earned: A = P (1 + rt )
Compound interest is interest earned/paid on both the interest and principal.
• Different Compounding Periods:
o annually:
m=1
o semi-annually: m = 2
o quarterly:
m=4
o monthly:
m = 12
o weekly:
m = 52
o daily:
m = 365
Continuous Compound Interest
• Formula: A = Pert
o A is the accumulated amount at the end of t years
o P is the principal
o e = 2.71828...
o r is annual interest rate in decimal form
o t is time in years
Effective Rate of Interest
• This is the simple interest rate that would produce the same amount of accumulated
interest in one year.
• Used as a basis for comparing interest rates.
• Equivalent to Annual Percentage Rate (APR) and Annual Percentage Yield (APY)
• When paying interest we want the lowest effective rate, and when earning interest we
want the highest effective rate.
5.2 Annuities
5.3 Amortization and Sinking Funds
Annuities
• An annuity is an account into which regular payments are made. Examples include
monthly mortgages and deposits into savings accounts.
Equity
• How much of the item belongs to you and not the bank.
• Equity = Value of the item – Amt owed to the bank
Amortize – to liquidate a debt by installment payments
• An amortization table can be used to summarize payments, equity, interest, principal, etc.
Sinking Fund – a fund set up for a specific purpose at some future date