SOLUTION: A deposit of $7,500.00 is placed in a savings account at an interest rate of 5% compounded continuously. Assuming no more deposits or withdrawals are made to the account, how long

Question 480925: A deposit of $7,500.00 is placed in a savings account at an interest rate of 5% compounded continuously. Assuming no more deposits or withdrawals are made to the account, how long will it take for the account balance to reach $10,000.00?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A deposit of $7,500.00 is placed in a savings account at an interest rate of 5% compounded continuously. Assuming no more deposits or withdrawals are made to the account, how long will it take for the account balance to reach $10,000.00?
**
Compound Interest Formula For Interest Compounded Continuously:
A=Pe^rt, P=initial investment, r=annual interest, A=amount after t years
..
10000=7500e^.05t
10000/7500=e^.05t
100/75=e^.05t
take log of both sides
ln(100/75)=.05t lne
log of base=1
.05t=ln(100/75)
t=ln(100/75)/.05
t=5.75 yrs
ans:
It willl take 5.75 years for the account balance to reach $10,000.00
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