Hidden Terms Lab

Introduction

In this lab, we are going to explore the differences in APR and APY and how this might affect our choices in banking and credit.

Part 1

Suppose you carry a balance of $1,000 on one credit card (CARD 1) that has a rate of 9% APR and another (CARD 2) with a rate of 15%. Assume you make no payments.

1. Using the formula for simple interest and the APR, find the total amount owed after one year.

Card 1: 1000 (.09)(1) = 1,090

Card 2: 1000(0.15)(1)= 1,150

2. Fill in the tables below using the amount owed as the principal for the next month. Use I = Prt to find the interest each month? Keep in mind that each month, only one month of time is passing. Round to the nearest cent (two decimal places).

CARD 1

CARD 2

Month

Principal

Interest = principal x rate x time

Amount owed

Principal

Interest = principal x rate x time

Amount owed

1

$1000

$7.50

$1007.50

$1000

$12.50

$1012.50

2

$1007.50

$7.56

$1015.06

$1012.50

$12.66

$1025.50

3

$1015.06

$7.61

$1022.67

$1025.16

$12.81

$1037.97

4

$1022.67

$7.67

$1030.34

$1037.97

$12.97

$1050.94

5

$1030.34

$7.73

$1038.07

$1050.94

$13.14

$1064.08

6

$1038.37

$7.79

$1045.86

$1064.08

$13.30

$1077.38

7

$1045.86

$7.84

$1053.70

$1077.38

$13.47

$1090.85

8

$1053.70

$7.90

$1061.60

$1090.85

$13.64

$1104.49

9

$1061.60

$7.96

$1069.56

$1104.49

$13.81

$1118.30

10

$1069.56

$8.02

$1077.58

$1118.30

$13.98

$1132.28

11

$1077.58

$8.08

$1085.66

$1132.28

$14.15

$1146.43

12

$1085.66

$8.14

$1093.80

$1146.43

$14.33

$1160.76

Total

$93.80

$160.76

3. How much interest in total do you pay for each card?

Card 1: $93.80

Card 2: $160.76

What was the effective annual interest rate for each card? (note: effective annual interest is the percent increase in the balance over one year) Round your percent to two decimal places.

Card 1: $93.80/100= 9.38%

Card 2: $160.76/100= 16.08%

4. Using the APY formula, find the APY for each credit card. (Your answer should be written in percent form rounded to two decimal places)

APY = [(1+APR/n)n - 1] x 100%

Card 1: [(1+.091212-1]x100%= 9.38%

Card 2: [(1+.151212 -1)]= 16.08%

5. What do you notice about your answers to #3 and #4?

What does this imply about APY?

6. What is the difference between APR and APY? Which is higher? By how many percentage points?

7. Using your answers in #1 & 3, what is the difference in the money paid in one year? (note: this is the difference compounding can make)

Part 2

Now, suppose you carry a balance of $12,000 on a credit card that has a rate of 18% APR

8. If you paid simple interest, how much interest would you pay in one year? Round to the nearest whole dollar.

$12,000 (0.18) (1)= $2,180

9. What is the APY on this card if you compound monthly? (Your answer should be in percent form rounded to two decimal places).

10. Now you will calculate the interest in two additional ways.

a. Use the simple interest formula and use APY instead of the APR for the rate. Round to the nearest whole dollar.

b. Use the compound interest formula and compound monthly with the APR for the rate. Round to the nearest whole dollar.

c. What do you notice about the two calculations? Why do you think this is?

d. How much more interest will you pay in one year, based on your calculations in 10 a & b than in 8?

11. Lenders typically advertise the APR for a credit card or loan. Why do they do this?