SOLUTION: 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 yo

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 What was the earliest date (day, month, and year) when you could have withdrawn $9,000?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.

RELATED QUESTIONS
Please help! I have worked on this challenge problem non stop for a while and I can not... (answered by Edwin McCravy)

You deposit $1000 into an account that pays 4.8% interest compounded quarterly. A. Write (answered by Alan3354)

Suppose you deposit $1000 in an account with an annual interest rate of 10% compounded... (answered by Boreal)

You deposit $9000 into an account with an APR of 3.6%. What is the balance in the account (answered by rfer)

Suppose you want to accumulate $50,000 for a college fund over the next 15 years.... (answered by ikleyn)

You make a one time deposit into an account earning 9.6% interest compounded... (answered by ikleyn)

Find the amount of money in a bank account given the following conditions. Initial... (answered by rfer,solver91311)

Over 2 years, how much more does $2000 in a savings account with an APR of 5.2%... (answered by TimothyLamb)

Please help me solve this problem: Jackson made an initial deposit of $900 to open a... (answered by jorel555)