Math 111 B & C --- Skills to Review for the Final

Look at the reviews for Midterms 1 and 2!!!

In addition to the material from the midterms, review the following:

1. Sequences:
• How to tell if a given sequence is additive, multiplicative or neither
• Know how to find and use recursive formulas for additive and multiplicative sequences

Ex: A(k+1) = A(k) + 5 or M(k+1) = 5 M(k) or M(k+3) = 5³ M(k)

· Be able to determine explicit formulas for additive and multiplicative sequences

· Understand the relationship between multiplier m and proportionate change p (m=p+1). Specifically, understand the two ways to get M(k+1) from M(k):

o M(k+1)=m M(k) (think: bacteria population)

o M(k+1)=M(k) + p M(k) (think: interest in an account)

· Know how to compute proportionate and percentage change.

2. Simple Interest (applies to the principal A(0) only):

The account balance after t interest periods at a rate of (r x 100)% is: A(t)=A(0)(1+rt).

3. Compounding Formulas
• CAF: A(k)=P (1 + r)^k (where P= initial quantity, k=# of compoundings and r=prop change)

Useful in population problems, or problems with accounts compounded annually (or with strange compounding periods).

• The general Compound Interest Formula:

Where A(0)=P=initial amount, r=yearly rate in decimal form, n=# of compoundings a year and t=#of years.

Use this if you’re given an annual rate and an indication of how many times a year the interest is compounded (eg, monthly).

Given enough information, you should be able to solve for:

a) A(t) (future values)

b) A(0)=P (present value)

c) Interest rate r

d) # of years t (requires natural log: be able to use it)

• Continuous Compounding:

Given enough information, you should be able to solve for:

a) A(t) (future values)

b) A(0)=P (present value)

c) rate r (requires natural log)

d) # of years t (requires natural log: be able to use it)

• Know how to compute the APY:

Understand that the APY is the percentage change in the balance of an account over a one-year period, and that it’s greater than or equal to the nominal annual interest rate listed by the bank.