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Lee deposits $200 every month into a savings account that earns 3.25% compounded monthly.
How many years would it take lee to reach his savings goal of $9000. keep 2 decimal places in your final anwser.
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First, I will solve this problem.
After finishing my solution, I will discuss on how the problem is posed, worded,
and what I think about all of this.
Use a standard formula for the future value of an ordinary annuity compounded monthly
FV =
where FV is the future value, P is the payment at the end of each month,
r is the nominal interest rate per year expressed as decimal,
n is the number of monthly deposits (of months).
So, we need to find " n " from this equation
= = = 45,
= .
Rewrite it in this form
= 0.121875,
= 1 + 0.121875 = 1.121875.
Take logarithm base 10 of both sides
n*log(1+0.0325/12) = log(1.121875)
and calculate
n = = 42.51952746 months.
Now we should round it to the closest greater integer number of months, which is 43 months,
in order for the bank would be in position to perform the last compounding at the end of the 43-th month.
43 months is the same as 3 years and 7 months.
ANSWER. The amount will exceed the goal of $9,000 in 43 months, or 3 years and 7 months.
Solved.
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The instruction to this problem, saying " keep 2 decimal places in your final answer ", is incorrect and non-sensical.
The answer to this problem should be expressed as an integer number of months.
Since the instruction is incorrect and non-sensical, it tells me that a person who created this problem,
is (1) unprofessional Math writer/composer and (2) is a random person in this field.
He or she is still able to re-write from other sources, but does not understand the meaning of the problem
and does not really understand what he/she writes or re-writes. It is very sad to me to see it and to tell it.
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I have been solving problems on this forum for many years.
I've seen dozens similar problems like
"how long does it take for a discretely compounded account to get an assigned value".
and I myself have probably solved about fifteen such problems at this forum.
But I have never seen such a problem formulated correctly at the forum.
They always asked for a final result "with two decimal places," which is meaningless in such problems,
where the final answer MUST be expressed in integer number of compounding periods.
Okay, I know, and you don't need to explain or refute it to me, that most of the incoming tasks
are intended for use as solutions on other websites or as a knowledge base for artificial intelligence.
But then, dear managers, you must ensure that you employ the most highly qualified people in the field.
However, what I see in the example of this task tells me the opposite - some of your employees do not meet
the high standards required for creating artificial intelligence.
And this is not just anywhere, but in the crucial matter of correctly formulating
the problem statement, where everything must be perfectly smooth and accurate.