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Question 959172: Tom and Louise wants to establish an account that will supplement their retirement income beginning 30 years from now. Suppose they can invest in a fund that pays 6% interest compounded quarterly.
a. What is the lump sum they must deposit today so that $500,000 will be available at time of retirement if the account pays?
b. If they deposit $10,000 in the account now, how long would it take their money to double?
Found 2 solutions by lwsshak3, ikleyn:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Tom and Louise wants to establish an account that will supplement their retirement income beginning 30 years from now. Suppose they can invest in a fund that pays 6% interest compounded quarterly.
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a. What is the lump sum they must deposit today so that $500,000 will be available at time of retirement if the account pays?
Compound Interest Formula: A=P(1+r/n)^nt, P=initial investment, r=interest rate, n=number of compounding periods per year, A=amount after t-years.
For given problem:
P=to find
r=.06
n=4
t=30
500000=P(1+.06/4)^(4*30)
500000=P(1+.015)^120
500000=P(1.015)^120
P=500000/(1.015)^120=83762
lump sum they must deposit today=$83,762
..
b. If they deposit $10,000 in the account now, how long would it take their money to double?
A/P=2=(1+r/n)^nt
2=(1.015)^4t
take log of both sides
ln2=4t*ln(1.015)
t=ln2/4ln(1.015)=11.6
how long would it take their money to double? about 12 years
Answer by ikleyn(53937)  (Show Source):
You can put this solution on YOUR website! .
Tom and Louise wants to establish an account that will supplement their retirement income beginning 30 years from now.
Suppose they can invest in a fund that pays 6% interest compounded quarterly.
a. What is the lump sum they must deposit today so that $500,000 will be available at time of retirement if the account pays?
b. If they deposit $10,000 in the account now, how long would it take their money to double?
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In his post, @lwsshar3 gave an answer "about 12 years" for question (b).
Actually, this problem admits and assumes a precise (not approximate) answer,
and this precise answer is DIFFERENT from approximate answer by @lwsshar3.
In this my post, I will explain how to get the correct answer.
b. If they deposit $10,000 in the account now, how long would it take their money to double?
A/P = 2 = (1+r/n)^nt
2 = (1.015)^4t
take log of both sides
ln(2) = 4t*ln(1.015)
t = ln(2)/4ln(1.015) ~ 11.6 years approximately.
11.6 years is approximately 11 years and 7.2 months.
This number we should round to 11 years and 9 months, when the bank will make his last compounding
at the end of the 3rd quarter of the 11th year.
So, the UNIQUELY correct and precisely accurate answer to the problem's question is 11 years and 9 months.
It is the time, when the amount at the account first time will get and exceed the doubled value of the principal.
This problem and the correct answer reveal immediately if a person, who solves the problem,
does really understand what he/she is doing.
Solved correctly with complete explanations.
Do not accept any other answer.
////////// I n t e r e s t i n g //////////
Today, May 14, 2026, at about 9:05 pm, I posted this problem to Google Overview Artificial Intelligence.
It practically reproduced the solution by @lwsshar3, giving the answer "approximately 11.64 years".
It shows that this AI does not understand what he/it is doing
and teaches visitors in WRONG WAY.
Ten minutes later, I posted this problem to another AI web-site, www.math-gpt.org/
It produced the same solution and the same answer as @lwsshar3
and also demonstrated that it does not understand what it is doing -
and teaches in WRONG WAY.
It is how the contemporary AI (plural) work in solving school Math problems:
it reminds me a railway, where explosive mines are buried in the ground at every 30 meters.
Obviously, for this class of problems, the base of solutions should be completely replaced
and the AIs should be re-trained from scratch.
It also tells me that those members in AI teams who allowed/(are responsible for) such situation,
do understand nothing in their job.
Let the managers of these project consider this my post as an alarm signal:
something is VERY WRONG in organization of their work process.
I even know - what precisely: there are wrong people in wrong positions,
and there is a lack of right people in right positions.
Also, the mechanism of selecting right people for right positions does not function properly.
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