This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Math 21B Kouba Discrete and Continuous Compound Interest
An Example of Exponential Growth DISCRETE COMPOUND INTEREST PROBLEM : Assume that P dollars is deposited in an account earning a compound interest rate of i computed
for each of m interest-earning periods. How much money A accumulates in
the account after these m periods ? Interest Period Total $ Accumulated
4 Pu+03+rPu+n3=Pu+aﬁr+a=Pu+n4 m A=P(1+i)m A PARTICULAR DISCRETE COMPOUND INTEREST PROBLEM : As- sume that P dollars is deposited in an account earning an annual interest
rate of r compounded n times per year for t years. How much money A
accumulates in the account after these t years ? . r .
Let 2 = a and m = nt, so that the above equatlon becomes : A=Pu+QM=P0+5YK n i.e., A=P(1+%)m. DISCRETE COMPOUND INTEREST PROBLEM BECOMES CONTIN-
UOUS COMPOUND INTEREST PROBLEM : RECALL : 1332) (1+7:-)k = e . LET n GO TO INFINITY FOR ..... A = P(1 + —)"‘ : A = lim P(1+ 1)," = lim P[(1 + -1—) in = P6" n-—>oo n n-)oo i.e., ...
View Full Document
- Spring '10