# Compounded Continuously

Discussion in 'Other Pre-University Math' started by nycmathguy, Oct 11, 2021.

1. ### nycmathguy

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Section 3.1
54 & 56 I need the formula needed to do this. Thanks.

nycmathguy, Oct 11, 2021

2. ### MathLover1

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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.

MathLover1, Oct 11, 2021
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3. ### nycmathguy

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nycmathguy, Oct 11, 2021
4. ### nycmathguy

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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

nycmathguy, Oct 12, 2021
5. ### MathLover1

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correct

MathLover1, Oct 12, 2021
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