Answer:
b) $17,400
d) $33,517.20
Step-by-step explanation:
a) $28,482.19 . . . . future value of all deposits
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b) The initial deposit was $3000, and there were 144 deposits of $100 each, for a total of ...
$3000 +144×100 = $17,400 . . . . total deposited
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c) $558.62
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d) 60 monthly withdrawals were made in the amount $558.62, for a total of ...
60×$558.62 = $33,517.20 . . . . total withdrawn
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<em>Additional information about (a) and (c)</em>
(a) The future value of the initial deposit is the deposit multiplied by the interest multiplier over the period.
A = P(1 +r/n)^(nt) = 3000(1 +.066/12)^(12·12) = 3000·1.0055^144 ≈ 6609.065
The future value of $100 deposits each month is the sum of the series of 144 terms with common ratio 1.0055 and initial value 100.
A = 100(1.055^144 -1)/0.0055 ≈ 21,873.123
So, the total future value is ...
$6609.065 +21873.123 ≈ $28482.188 ≈ $28,482.19
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(c) The withdrawal amount can be found using the same formula used for loan payments:
A = P(r/n)/(1 -(1 +r/n)^(-nt)) = $28482.19(.0055)/(1 -1.0055^-60) ≈ $558.62
