Compounded Continuously

Section 3.1
54 & 56



I need the formula needed to do this. Thanks.

 

The continuous compounding formula says A = Pe^(rt ) where 'r' is the rate of interest.
For example, if the rate of interest is given to be 10% then we take r = 10/100 = 0.1.

Example : Jim invested $5000 in a bank that pays an annual interest rate of 9% compounded continuously. What is the amount he can get after 15 years from the bank? Round your answer to the nearest integer.

Solution:

To find: The amount after 15 years.

The initial amount is P = $5000.

The interest rate is, r = 9% = 9/100 = 0.09.

Time is, t = 15 years.

Substitute these values in the continuous compounding formula,

A = Pe^(rt)

A = 5000 * e^(0.09*15)) ≈ 19287

The answer is calculated using the calculator and is rounded to the nearest integer.

Answer: The amount after 15 years = $19,287.

 

I will use your sample questions to answer 54 & 56.

 

Question 54

I will do 54 for t = 10 only.

A = Pe^(rt)

A = (12,000)e^(0.06)(10)

A = $21,865.4256

A = $21,865.43

Question 56

I will do 56 for t = 20 only.

A = Pe^(rt)

A = (12,000)e^(0.035)(20)

A = $24,165.03249

A = $24,165.03

 

correct

 

You see, one course at a time works best for me.