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Cedric has deposited 12,000 into an account that pays 5% interest compounded annually.

Daniel has deposited 12,000 into an account that pays 7% interest compounded annually.

In 15 years Cedric and Daniel compare their respective balances. To the nearest dollar, what is the positive difference between their balances?

 Feb 17, 2021
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A = P(1 + r/n)nt

 

where,

A = final amount

P = initial investment 

r = interest rate

n = number of times interest is applied

t = number of time periods

 

Cedric:
A = P(1 + r/n)nt

   = 12000(1 + 0.05/1)(1*15)

   = 12000(1.05)15

   ≈ 12000(2.0789)

   ≈ $24 947.14

 

Daniel:
A = P(1 + r/n)nt

   = 12000(1 + 0.07/1)(1*15)   

   = 12000(1.07)15

   ≈ 12000(2.759)

   ≈ $33 108.38

 

33108.38 - 24947.14 = $8161.24, which is your answer :)

 Feb 17, 2021

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