1. 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?

2. 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

3. 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

4. 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)

5. 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 $7373.93 and a closing balance (A) of $7382.59 for 28 days (n). What is the APY assuming daily compounding? Compounded daily for 1 year (365 days)

6. 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  103.04 - 100 3.04

7. 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

8. 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 years @ 12 months per year = 36 r = 0.15  0.292 29.2%!!!

9. 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 $384.00 for 60 months. What is the APR (to nearest 10 th of percent? n = 60 monthsr = ? I = A – P A = 384(60) = 23040 -18436 4604 I = Prt 4604 = 18436(r)5r = 0.0499457583  0.098 9.8%

10. 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) = 48.60 – interest to be paid

11. 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 0.057553% per day  21.1% APR