CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 13. Finance

Vocabulary

Nominal interestis a number that resembles an interest rate, but it really is a sum of compound interest rates. A
nominal rate of 12% compounded monthly is really 1% compounded 12 times.
( 1 +. 12
12

) (^12) = ( 1 + 0. 01 ) (^12) = 1. 1286
Thenumber of compounding periodsis how often the interest will be accrued and added to the account balance,
and is represented by the variablek.
Guided Practice

1. How much will Steve have in 8 years if he invests $500 in a bank that offers 8% compounded quarterly?


2. How many years will Mark need to invest his money at 3% compounded weekly(k= 52 )if he wants his $100 to
   grow to $400?


3. What nominal interest rate compounded semi-annually doubles money in 18 years?
   Answers:
   1.PV= 500 ,t= 8 ,i=8%,FV=?,k= 4

FV=PV( 1 +ki)kt= 500 ( 1 +^0. 408 )^4 ·^8 =$942. 27
2.FV= 400 ,PV= 100 ,k= 52 ,i= 0. 03 ,t=?

FV=PV

(

1 +ki

)kt

400 = 100

(

1 +^052.^03

) 52 ·t

t= 52 ·ln(ln 4 1 + 0. 03

52

)= 46. 22 years

3.PV= 100 ,FV= 200 ,t= 18 ,k= 2 ,i=?

FV=PV

(

1 +ki

)kt

200 = 100

(

1 + 2 i

) 2 · 18

i= 2

(

2361 − 1

)

≈ 0. 03888 = 3 .888%

Practice

1. What is the length of a compounding period ifk=12?


2. What is the length of a compounding period ifk=365?


3. What would the value ofkbe if interest was compounded every hour?


4. What would the value ofkbe if interest was compounded every minute?


5. What would the value ofkbe if interest was compounded every second?