Suppose an individual makes an initial investment of $3,000 in an account that earns 6.6%, compounded monthly, and makes additional contributions of $100 at the end of each month for a period of 12 years. After these 12 years, this individual wants to make withdrawals at the end of each month for the next 5 years (so that the account balance will be reduced to $0). (Round your answers to the nearest cent.)(a) How much is in the account after the last deposit is made?
(b) How much was deposited?
(c) What is the amount of each withdrawal?
(d) What is the total amount withdrawn?
I get A and C. If you could explain B and D I'd appreciate it.
Answers
Answer:
b) $17,400
d) $33,517.20
Step-by-step explanation:
a) $28,482.19 . . . . future value of all deposits
__
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
__
c) $558.62
__
d) 60 monthly withdrawals were made in the amount $558.62, for a total of ...
60×$558.62 = $33,517.20 . . . . total withdrawn
_____
Additional information about (a) and (c)
(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
__
(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
Final answer:
The total amount deposited in the account was $17,400 including an initial investment of $3,000 and subsequent monthly payments of $100 for 12 years. The total amount withdrawn was equal to the final balance after the last deposit.
Explanation:
Let's tackle each question one by one:
- You've mentioned that you have already figured out part (a) and (c), so let's move on to part (b).
- (b) How much was deposited?The individual started with an initial deposit of $3,000. After that, they deposited $100 at the end of each month for 12 years. That's 12 years * 12 months/year * $100/month, for a total of $14,400. So, if you add the initial deposit, the total amount deposited over the whole period is $3,000 + $14,400 = $17,400.
- (d) What is the total amount withdrawn?The total amount withdrawn is the same as the final balance of the account after the last deposit, as the question states the account balance will be zero after the withdrawals. Since you have already figured out part (a) which is the account balance after the last deposit, the total amount withdrawn corresponds to that sum.
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Answer:
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Step-by-step explanation:
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i assume ur asking for how much is left over
250-35= 215
215-75= 140
$140 left
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
Notice vocabulary:
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Answers
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Energy used by the oven Kw-hrs
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