3. Joe and Sue invested $2000 at Bank America in 1995, at 6% compounded quarterly. In the year 2000
they moved to another city and took the total money from their first investment added $500 and invested it at Bank Bravo, at 7% compounded quarterly.
a. What is the value of this account now in 2004?
amount in 2000
= 2000(1.015)^20
= 2693.71
plus the extra 500 in year 2000
=3193.71
This will earn for 4 years
final amount
= 3193.71(1.0175)^16
= 4215.47
To calculate the value of the account in 2004, we need to calculate the values of each investment separately and then add them together.
First, let's calculate the value of the initial investment at Bank America from 1995 to 2000. Since the interest is compounded quarterly, we'll use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principle amount (initial investment)
r = Annual interest rate (6% or 0.06 as a decimal)
n = Number of times interest is compounded per year (4, for quarterly compounding)
t = Number of years (2000 - 1995 = 5)
Using these values, we can calculate the value of the initial investment at Bank America in 2000:
A = 2000(1 + 0.06/4)^(4*5)
A = 2000(1 + 0.015)^20
A ≈ 2000(1.015)^20
A ≈ 2000(1.34866)
A ≈ 2697.32
So, the value of their investment in 2000 after moving to another city is approximately $2697.32.
Now, let's calculate the value of the additional investment at Bank Bravo from 2000 to 2004. Using the same compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principle amount (additional investment of $500)
r = Annual interest rate (7% or 0.07 as a decimal)
n = Number of times interest is compounded per year (4, for quarterly compounding)
t = Number of years (2004 - 2000 = 4)
Using these values, we can calculate the value of the additional investment at Bank Bravo in 2004:
A = 500(1 + 0.07/4)^(4*4)
A = 500(1 + 0.0175)^16
A ≈ 500(1.0175)^16
A ≈ 500(1.31277)
A ≈ 656.39
So, the value of their additional investment in 2004 at Bank Bravo is approximately $656.39.
Finally, to find the total value of both investments, we add the values from each investment:
Total Value = Value of initial investment + Value of additional investment
Total Value = $2697.32 + $656.39
Total Value ≈ $3353.71
Therefore, the value of the account in 2004 is approximately $3353.71.