SOLUTION: I reaally need help with this ~Joe deposits $1,500 in an account that pays 3% annual interest compounded continuously. a.How much will Joe have in his account after 5 years? b.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I reaally need help with this ~Joe deposits $1,500 in an account that pays 3% annual interest compounded continuously. a.How much will Joe have in his account after 5 years? b.       Log On


   

Question 1017116: I reaally need help with this
~Joe deposits $1,500 in an account that pays 3% annual interest compounded continuously.
a.How much will Joe have in his account after 5 years?
b. How long will it take Joe to double his money?
Use natural logarithms and explain your answer.
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for interest compounded continuously is
:
A = Pe^(rt) where P is the initial amount, r is the rate, t is time in years
:
a) A = 1500e^(0.03 * 5) = 1500e^(0.15)
use definition of logarithm
0.15 = ln(A / 1500)
0.15 = ln(A) - ln(1500)
ln(A) = 0.15 + ln(1500) = 0.15 + 7.313220387 = 7.463220387
A = e^(7.463220387) = 1742.751361739
Note that e = 2.718281828
Therefore Joe has $1742.75 in his account after 5 years
:
b) 3000 = 1500e^(0.03t)
use definition of logarithm
0.03t = ln(2)
t = ln(2) / 0.03 = 0.693147181 / 0.03 = 23.104906019
Therefore Joe will double his money in 23.1 years
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