Download Math 111: Skills Review for Final Exam - Sequences, Simple and Compounded Interest - Prof. and more Study notes Mathematics in PDF only on Docsity! Math 111--- Skills to Review for the Final Look at the reviews for Midterms 1 and 2!!! Besides the material from the two midterms, review the following skills: 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: p=m-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 % change over a given time period. 2. Simple Interest (interest is applied to the principal P only): The account balance after t interest periods at a rate of r x 100% is: A(t)=P(1+rt). 3. Compounded Interest Formulas (interest is applied to the entire balance each time) • 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 CAF (discretely compounded interest): nt n r PtA += 1)( (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: A(t)=P ert . 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 1001 )0( )1( 100)1( × −=×−= A A mAPY 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.
