Question

Darcy keeps $5,000 in a bank account that does not earn any interest. Every week, she withdraws 10 percent of the money in the account for spending. To the nearest cent, how much has she withdrawn in total after 8 weeks ?

(A) $2610.78 (B) $2638.08 (C) $2755.28 (D) $2847.66

Answer 1

Answer:

(D) $2847.66

Step-by-step explanation:

Because Darcy withdraws 10% of the money in the account every week, this problem comes under the concept of compound interest.

Because the money in the account is decaying every week, the compound interest formula can be used with a negative sign as shown below.

A  =  P(1 - r)n

P ----> Initial deposit

A ----> Final value of the deposit after 'n' weeks

r ---> Percent of decay

Substitute the values in the above formula.

A  =  5000(1 - 0.1)8

A  =  5000(0.9)8

A  =  5000(0.43046721)

A  ≈  2152.34

The account balance after 8 weeks is about $2152.34.

Amount of money she has withdrawn in total after 8 weeks :

=  $5000 - $2152.34

=  $2847.66

Hence, Darcy has withdrawn $2847.66 in total after 8 weeks.

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Answered by: ms115

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