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