CK-12-Pre-Calculus Concepts

13.5. APR and APY (Nominal and Effective Rates) http://www.ck12.org

FV=PV

(

1 +ki

)kt

104. 08 = 100

(

1 + 12 i

) 12

i= 12

[(

104. 08

100

) 121

− 1

]

= 0. 0400667

The second bank will need to offer slightly more than 4% to match the first bank.
Concept Problem Revisited
A loan that offers 2.5% APR that compounds monthly is really charging slightly more.
( 1 + 0. 025
12

) (^12) ≈ 1. 025288
They are really charging about 2.529%.
The table below shows the APY calculations for three different banks offering 8.1% annually, 8% compounded
monthly and 7.9% compounded continuously.
TABLE13.8:
Bank A Bank B Bank C
FV=PV( 1 +i)t
FV= 100 ( 1 + 0. 081 )
FV=$108. 1

APY= 8 .1 %

FV=PV

(

1 +ki

)kt

FV= 100

(

1 +^012.^08

) 12

FV≈ 108. 299

APY≈ 8 .300%

FV=PV·ert

FV= 100 e^0.^079

FV&≈ 108. 22

APY≈ 8 .22%

Even though Bank B does not seem to offer the best interest rate, or the most advantageous compounding strategy,
it still offers the highest yield to the consumer.

Vocabulary

Nominal Interest Rateis an interest rate in name only since a method of compounding needs to be associated with
it in order to get a true effective interest rate. APRrates are nominal.
Annual Effective Interest Rateis the true interest that is being charged or earned. APYrates are effective.

Guided Practice

1. Which bank offers the best deal to someone wishing to deposit money?
   
   
   • Bank A, offering 4.5% annually compounded
   
   
   • Bank B, offering 4.4% compounded quarterly
   
   
   • Bank C, offering 4.3% compounding continuously