Continuous Compounding
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Compound Interest Equation
A = P(1+  )n•t
Continuous Compounding
(1+  )= er
n
r
n
r
Continuous Compounding
A = Per•t

A comparison question relating quarterly compounding to

continuous compounding.

If you invest $2,000 at an annual interest rate of
9% compounded quarterly, calculate the finalamount you will have in he account after 20 years.
P=$2000, r = 0.09, n=4, t=20
A = 2000(1+        )4•20
A = $11,860.29
Compound Interest Equation
0.09
Continuous Compounding
4
If you invest $2,000 at an annual interest rate of
9% compounded continuously, calculate the final
amount you will have in he account after 20 years.
P=$2000, r = 0.09, t=20
A = 2000e0.09•20
A = $12,099.29
Continuous Compounding
more!!
Answer (to the nearest dollar): $
If you invest $1,000 at an annual interest rate of 5% compounded
continuously, calculate the final amount you will have in the account
after 5 years.
P =

r =

t =
in years
as a decimal with a leading zero: 5% written as 0.05
no commas or $
Continuous Compounding
A = Per•t

Assume you invest $5,000 in an account paying 8% interest compounded

continuously. How much money will be in the account after 5 years?

Answer (to the nearest dollar): $
P =

r =

t =
in years
as a decimal with a leading zero: 5% written as 0.05
no commas or $
Continuous Compounding
A = Per•t

Find the amount of money you will have after 10 years if $15,000 is

invested in accounts paying 6% interest compounded continuously.

Answer (to the nearest dollar): $
P =

r =

t =
in years
as a decimal
no commas or $
Continuous Compounding
A = Per•t

Find the amount of money in the account after 18 years if Rebecca

invested $15,000 into an account that pays 10% interest compounded

continuously.

Answer (to the nearest dollar): $
P =

r =

t =
in years
as a decimal with a leading zero: 5% written as 0.05
no commas or $
Continuous Compounding
A = Per•t

How much money will you have if you invest $4000 in a bank for sixty

years at an annual interest rate of 9%, compounded continuously?

Answer (to the nearest dollar): $
P =

r =

t =
in years
as a decimal with a leading zero: 5% written as 0.05
no commas or $
Continuous Compounding
A = Per•t

Find the amount of money you will have after 18 years if $2,000 is

invested in accounts paying 5% interest compounded continuously.

Answer (to the nearest dollar): $
P =

r =

t =
in years
as a decimal with a leading zero: 5% written as 0.05
no commas or $
Continuous Compounding
A = Per•t

Find the amount of money you will have after 30 years if $5,000 is

invested in accounts paying 8% interest compounded continuously.

Answer (to the nearest dollar): $
P =

r =

t =
in years
as a decimal with a leading zero: 5% written as 0.05
no commas or $
Continuous Compounding
A = Per•t

If you invest $10,000 for two years at an annual rate of 8%, compounded

continuously, how much INTEREST will you make during the two years?

remember, I only want the interest earned, not the total in the account.
Answer (to the nearest dollar): $
P =

r =

t =
in years
as a decimal with a leading zero: 5% written as 0.05
no commas or $
Continuous Compounding
A = Per•t

If the world population is about 6 billion people now and if the

population grows continuously at an annual rate of 1.7%, what will the

population be in 10 years?

Answer (to two decimals): 
P =

r =

t =
billion
in years
as a decimal with a leading zero: 5% written as 0.05
Continuous Compounding
billion
A = Per•t

Derek invested $1,500 into an account that pays 9% interest

compounded continuously. How long must the money be left in the

account for it to grow to $4,417?

Answer (to the nearest whole year):
P =

r =

t =
? ? ? ?
Use trial and error to find the value for t (or use logs!)
in years
as a decimal with a leading zero: 5% written as 0.05
no commas or $
Continuous Compounding
A = Per•t
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