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?

Guest Feb 17, 2021

#1**0 **

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 :)

Logarhythm Feb 17, 2021