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.
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?
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.
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.