CK-12-Pre-Calculus Concepts

13.3. Compound Interest per Period http://www.ck12.org

Note: A very common mistake when typing the values into a calculator is using an exponent of 12 and then
multiplying the whole quantity by 4 instead of using an exponent of( 12 · 4 ) = 48.
Example B
How many years will Matt need to invest his money at 6% compounded daily(k= 365 )if he wants his $3,000 to
grow to $5,000?
Solution:FV= 5 , 000 ,PV= 3 , 000 ,k= 365 ,i= 0. 06 ,t=?

FV=PV

(

1 +ki

)kt

5 , 000 = 3 , 000

(

1 +^0365.^06

) 365 t

5

3 =

(

1 +^0365.^06

) 365 t

ln^53 =ln

(

1 +^0365.^06

) 365 t

ln^53 = 365 t·ln

(

1 +^0365.^06

)

t= ln

(^53)
365 ·( 1 +^0365.^06 )=^8.^514 years
Example C
What nominal interest rate compounded quarterly doubles money in 5 years?
Solution:FV= 200 ,PV= 100 ,k= 4 ,i=?,t= 5

FV=PV

(

1 +ki

)kt

200 = 100

(

1 + 4 i

) 4 · 5

(^201) =

[(

1 + 4 i

) 20 ] 201

2201 = 1 + 4 i

i=

(

2201 − 1

)

4 ≈ 0. 1411 = 14 .11%

Concept Problem Revisited
If Clever Carol earned the 12% at the end of the year she would earn $12 in interest in the first year. If she compounds
itk=2 times per year then she will end up earning:

FV=PV( 1 +ki)kt= 100 ( 1 +.^122 )^2 ·^1 =$112. 36