Joe and Susan invested $1500 at Bank of America in 2000, at 4% compounded quarterly. In the year 2005 they moved to another city and took the total money from their investment added $500 and invested in at Bank Bravo, at 5% compounded quarterly.

a) What is the value of this account now in 2010? Show all steps arriving to your answer.
b) What is the total amount of compound interest earned?

To find the value of the account in 2010, we'll break down the problem into two parts: the first investment at Bank of America from 2000 to 2005, and the second investment at Bank Bravo from 2005 to 2010.

Part 1: Investment at Bank of America (2000-2005)
To calculate the value of their investment from 2000 to 2005, we'll use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = Final amount
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years

In this case, the principal amount (P) is $1500, the annual interest rate (r) is 4% (or 0.04), and the interest is compounded quarterly, so the number of times compounded per year (n) is 4. The time period (t) is 5 years. Plugging in these values into the formula, we get:

A1 = $1500(1 + 0.04/4)^(4*5)
= $1500(1 + 0.01)^(20)
= $1500(1.01)^(20)
≈ $1819.39

So, the value of their investment at Bank of America in 2005 was approximately $1819.39.

Part 2: Investment at Bank Bravo (2005-2010)
Now, they took the total money of $1819.39 from their Bank of America investment, added $500, and invested it in Bank Bravo. Using the same formula, but with a different principal amount (P) and annual interest rate (r), we can calculate the value of their investment from 2005 to 2010.

P2 = $1819.39 + $500 = $2319.39 (Principal amount for Bank Bravo)
r2 = 5% = 0.05 (Annual interest rate for Bank Bravo)

A2 = $2319.39(1 + 0.05/4)^(4*5)
= $2319.39(1 + 0.0125)^(20)
= $2319.39(1.0125)^(20)
≈ $3100.04

Therefore, the value of their account in 2010 is approximately $3100.04.

b) To calculate the total amount of compound interest earned, we need to find the difference between the final amount (A2) and the total amount invested ($1500 + $500) over the entire period (2000-2010).

Total interest = A2 - (P + $500)
= $3100.04 - ($1500 + $500)
= $3100.04 - $2000
= $1100.04

So, the total amount of compound interest earned over the entire period is $1100.04.

P = Po * (1+r)^n

r = (4%/4)/100% = 0.01 = Quarterly % rate expressed as a decimal.

n = 4Comp./yr. * 5yrs. = 20 Compounding
periods.

Solve for P.

2nd investment = P + $500 @ 5% for 5 yrs.