Question 1060720: You save money in the following way:
• Jan 1, 2000: Deposit an unknown amount of money into a new account A with an APR of 3% compounded quarterly.
• Jan 1, 2005: Withdraw all your money from account A and deposit it and an additional $5,000 into a new account B with an APR of 5.5% compounded continuously.
• Jan 1, 2012: Account B has a balance of $10,078.46.
Answer the following questions:
1. What was the amount you deposited into account A on Jan 1, 2000?
2. What was the earliest date (day, month, and year) when you could have withdrawn $9,000?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x is deposited
A=x(1+(.03/4))^20, the 20 coming from 5 years at 4 times a year compounded.
A=1.161 x, but don't round
Now add 5000 to it so it is 1.161 x +5000
This is compounded continuously at 5.5% or 0.055 for 7 years
A=10078.46
That equals x*e^rt, where rt=0.385, 0.055*7
e^0.385=1.4696. Still don't round.
We now know that (1.161x+5000)*1.4696=10078.46
Can divide by the e value we just had, and that was the amount that we had the first five years
6857.89, and then subtract the 5000 added to get 1857.89.
Then divide by the 1.161 x and get $1600. ANSWER
Check
1600(1+(0.03/4))^20=1857.89
add $5000
$6857.89*e(.385)=$10,078.46
It reached $9000 after t number of years when e^(.055t)*6857.89=9000.
Divide by 6857.89 and get 1.31236, don't round
e^(0.055t)=1.31236
ln both sides
0.055t=0.27182
Divide by 0.055 and t=4.9422 years. Subtract 4 and multiply by 365.
343.92 or 344 days.
It would have been 344 days into 2009 or 10 December 2009.
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