Answer: $4,914
Explanation:
To calculate the final balance in Brandon's account, we need to use the formula for compound interest: A = P(1 + r/n)^(nt)
where A is the final balance, P is the initial investment, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we have:
P = $11,000
r = 1% = 0.01
n = 4 (because the interest is compounded quarterly)
t = 20
so, A = $11,000(1 + 0.01/4)^(4*20) = $11,000(1.0025)^80 = $22,817.20
To calculate the final balance in Robert's account, we need to use the same formula, but with different values for r, n, and t.
In this case, we have:
P = $11,000
r = 13/100 = 0.13
n = 12 (because the interest is compounded monthly)
t = 20
so, A = $11,000(1 + 0.13/12)^(12*20) = $11,000(1.01083333)^240 = $27,731.34
To find the difference in the final balances, we subtract the final balance in Brandon's account from the final balance in Robert's account:
$27,731.34 - $22,817.20 = $4,914.14
To the nearest dollar, the difference is $4,914.