Aim: Money Matters – Effective Rate & APR Course: Math Literacy Aim: How does money matter? The lowdown on interest rates. Do Now: Annie deposits $1000 in a local bank at 8% interest for 1 year. How much does Annie have in her account after 1 year? Annie deposits $1000 in a local bank at 8% interest for 1 year compounded quarterly. How much does Annie have in her account after 1 year?

Aim: Money Matters – Effective Rate & APR Course: Math Literacy Simple & Exponential Money Exponential growth Compound Interest Simple annual interest A = P(1 + r) t Exponential growth Continuous compounding A – ending amount also referred to an Future Value or Maturity Value P – beginning amount also referred to an Present Value I = A – P Interest earned is the difference between Future Value and Present Value Simple InterestI = PrtA = P + I

Aim: Money Matters – Effective Rate & APR Course: Math Literacy Effective Rate/Annual Percentage Yield When compounding takes place we often would like to know the Effective Rate. For interest rate i per compounding period, a principal of $1 grows to (1 + i) n in n periods. interest rate for compounded period Also called

Aim: Money Matters – Effective Rate & APR Course: Math Literacy Model Problem With a nominal annual rate of 6% compounded monthly, what is the APY? (Effective Rate)

Aim: Money Matters – Effective Rate & APR Course: Math Literacy Model Problem Suppose that the monthly statement from the fund reports a beginning balance (P) of $ and a closing balance (A) of $ for 28 days (n). What is the APY assuming daily compounding? Compounded daily for 1 year (365 days)

Aim: Money Matters – Effective Rate & APR Course: Math Literacy Model Problem A credit union offers a certificate of deposit at an annual interest rate of 3%, compounded monthly. Find the effective rate. Round to nearest 100 th of a percent. (Effective Rate) = 3.04% I = A – P A 

Aim: Money Matters – Effective Rate & APR Course: Math Literacy Annual Percentage Rate (APR) Annual Percentage Rate (APR) – the rate paid on a loan when that rate is based on the actual amount owed for the length of time that it is owed. It can be found for interest rate r, with N payments by using the formula The cost of credit! 1969 Truth in Lending Act interest calculated only on the amount you owed at particular time not on original amount

Aim: Money Matters – Effective Rate & APR Course: Math Literacy Model Problem You’re considering buying a computer for a price of $1399, to be paid in monthly installments over 3 years at a rate of 15%. What is the APR? n = 3 12 months per year = 36 r = 0.15  %!!!

Aim: Money Matters – Effective Rate & APR Course: Math Literacy Model Problem A Blazer with a price of $18,436 is advertised at a monthly payment of $ for 60 months. What is the APR (to nearest 10 th of percent? n = 60 monthsr = ? I = A – P A = 384(60) = I = Prt 4604 = 18436(r)5r =  %

Aim: Money Matters – Effective Rate & APR Course: Math Literacy Model Problem You purchase a refrigerator for $675. You pay 20% down and agree to repay the balance in 12 equal monthly payments. the finance charge on the balance is 9% simple interest. a)Find the finance charge b)Estimate the annual percentage rate. I = Prt 16.6% 675(.20) = 135 – down payment 675 – 135 = 540 – amount to be financed a) I = 540(0.09)(1) = – interest to be paid

Aim: Money Matters – Effective Rate & APR Course: Math Literacy Open-Ended Credit-Comparing APRs Credit cards are convenient, but can lead to trouble! Compare APRs to find the best deal. Find the APR for a rate of 1½% per month Find the APR for a rate of % per day  21.1% APR