Joe and Sue invested $1500 at Bank America in 2000, at 4% compounded quarterly. In the year 2005
they moved to another city and took the total money from their first investment added $500 and invested it at Bank Bravo, at 5% compounded quarterly.
a. What is the value of this account now in 2010?
b. What is the total amount of compound interest earned?
(1500(1+.04/4)^(4*5) + 500)(1+.05/4)^(4*5) = 2987.51
2987.51 - (1500+500) = 987.51
330.29 on the 1st deposit
657.22 on the 2nd deposit
To find the value of the account in 2010, we first need to calculate the value of the initial investment at Bank America in 2005. We can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal (initial investment)
r is the annual interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the number of years
For the investment at Bank America in 2000:
P = $1500
r = 4% = 0.04
n = 4 (compounded quarterly)
t = 5 (from 2000 to 2005)
First, we calculate the value of the initial investment in 2005:
A_2005 = $1500(1 + 0.04/4)^(4*5)
A_2005 = $1500(1 + 0.01)^(20)
A_2005 = $1500(1.01)^(20)
A_2005 = $1500 * 1.216653...
A_2005 ≈ $1,824.98
Next, we add $500 to the value of the investment in 2005 and calculate the interest at Bank Bravo:
P = $1,824.98 + $500 = $2,324.98
r = 5% = 0.05
n = 4 (compounded quarterly)
t = 5 (from 2005 to 2010)
A_2010 = $2,324.98(1 + 0.05/4)^(4*5)
A_2010 = $2,324.98(1 + 0.0125)^(20)
A_2010 = $2,324.98(1.0125)^(20)
A_2010 = $2,324.98 * 1.281386...
A_2010 ≈ $2,977.90
Therefore, the value of the account in 2010 is approximately $2,977.90.
To calculate the total amount of compound interest earned, we subtract the initial investment from the final amount:
Interest = Final amount - Initial investment
Interest = $2,977.90 - $1500 - $500
Interest = $977.90
Therefore, the total amount of compound interest earned is $977.90.