{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Interest

# Interest - Math 21B Kouba Discrete and Continuous Compound...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the 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 1 P+i-P=P(1+i) 2 P(1+z‘)+z‘-P(1+z‘)=P(1+z‘)(1+z‘)=P(1+i)2 3 P0+OI+LPU+02=PU+QHL+Q=P0+U3 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

{[ snackBarMessage ]}

### Page1 / 2

Interest - Math 21B Kouba Discrete and Continuous Compound...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online