Section+3.6

=Section 3.6=

Formulas
Future Value of Annuity Payment to Achieve Goal Loan Payment

FV= Pmt { [ (1+r/n)^nt -1] / (r/n) } Pmt = FV { (r/n) / [ ( 1+ r/n)^nt -1 ]} Pmt = P(r/n) / 1- (1+r/n)^ -nt

Mathematics of Finance
Compounding Interest A=p(1+r/n)^nt A= amount p= principle r= annual interest rate (APR) t= time in years n= number of times compounded in a year
 * The interest becomes part of the investment so that interest is earned on the interest itself.

Example: Invest $500 at 9% APR compounded monthly. What is the balance in 5 years? A= 500(1+(.09/12))^12*5 A= 500(1.57) A= $782.84

Compounding Continuously A= Pe^rt

Annual Percentage Yield (APY): The percentage rate that compounded annually would yield the same return as the given interest rate with the given compounding period.

Example: What is the APY for an investment which earns 8.75% compounded quarterly? A = P(1+r/n)^nt [p(1+r/1)^1(1)]/p = [p(1+.0875/4)^4(1)]/p 1+r = (1+.0875/4)^4 r = (1+.0875/4)^4-1 r = 9.041%

Annuities- Future Values
Annuity: A sequence of equal period payments

Future Value: The net amount of money returned from an annuity

Example: FV = $1,000,000 Time = 42 years APR= 8% compounded 26 times a year What do I need to contribute from each paycheck? Pmt = (1,000,000)( .08 / (1 + .08/26)^ 26*42 -1] Pmt = $111.32

Homework
p. 345 # 27-61 odd and # 71-79 odd p. 341 # 7-56 multiples of 7