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Question 1008342: If we have $4000 to put in the bank earning 4.5 % interest compounded 2 times per year; how long will it take before we double our money?
Your money would double in years.
If we have $P o to put in the bank earning 4.5 % interest compounded 2 times per year; how long will it take before we double our money?
Your money would double in years
Found 2 solutions by lwsshak3, ikleyn:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! If we have $4000 to put in the bank earning 4.5 % interest compounded 2 times per year; how long will it take before we double our money?
Your money would double in years.
If we have $P o to put in the bank earning 4.5 % interest compounded 2 times per year; how long will it take before we double our money?
Your money would double in years
Compound interest formula: A=P(1+r/n)^nt,P=initial investment, r=interest rate, n=number of compounding periods per year, A=amt after t-yrs
First problem:
P=4000
r=.045
n=2
A/P=2=(1+.045/2)^2t
2=(1.0225)^2t
log 2=2tlog(1.0225)
take log of both sides
2t=log2/log(1.0225)=31.15
t=15.6 yrs
how long will it take before we double our money? 15.6 yrs
2nd problem: same answer as first problem.(note:amt of initial investment does not matter)
Answer by ikleyn(53878)  (Show Source):
You can put this solution on YOUR website! .
If we have $4000 to put in the bank earning 4.5 % interest compounded 2 times per year;
how long will it take before we double our money?
Your money would double in how many years?
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Formal calculations in the post by @lwsshak3 are correct and lead to value
time = 15.6 years approximately. It is about 15 years and 7 months.
But his interpretation of this value is incorrect and contradicts to the meaning of the problem.
We will not get the doubled amount in 15 years and 7 months from the bank,
because the bank will make the last relevant compounding only after 16 years.
16 years is the closest time when the amount first time will get and will overcome the doubled value.
It is because the amount at the account IS NOT a continuous exponential function of time.
The continuous exponential function is only approximation to the real function, which is piecewise constant
and changes the values only at the ends of compounding periods, i.e. semi-annually.
So, the correct answer in this problem is not 15.6 years: the correct answer is 16 years.
I saw similar incorrect interpretation many times (uncounted number of times)
at this forum from different tutors.
They all as one person make and repeat the same error.
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Such uniformity in the repetition of the very same error simply shocks me.
It turns out that so-called tutors — people who are, in many other aspects, perfectly normal individuals
— are, on this particular issue, completely incapable of independent thought.
There is a certain mystery here for me.
Today, April 28, 2026, I submitted this problem to two artificial intelligence web-sites:
one to Google Overview and other to math-gpt.org - for checking purposes.
Both web-sites returned incorrect answers, identical to the incorrect solution provided by @lwsshak3.
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It CONFIRMS the fact that the whole community of tutors
INCORRECTLY treats all similar problems
and incorrectly teaches the students.
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