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Brandon invested $11,000 in an account paying an interest rate of 1% compounded

quarterly. Robert invested $11,000 in an account paying an interest rate of 13/%
compounded monthly. After 20 years, how much more money would Robert have in
his account than Brandon, to the nearest dollar?

2 Answers

0 votes

Answer:391

Explanation:

User Iwalkbarefoot
by
8.9k points
5 votes

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.

User Weakdan
by
7.8k points

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