SOLUTION: Compound Interest formula: A= P(1+(r/n))^nt I have to use this formula to answer this question: Determine how much time is required for an investment to double in value if int

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Question 481218: Compound Interest formula:
A= P(1+(r/n))^nt
I have to use this formula to answer this question:
Determine how much time is required for an investment to double in value if interest is earned at a rate of 6.25% and compounded annually?
Please give me a detailed answer, I have tried using the formula myself but I keep getting stuck and am not having much success.
Thank you in advance for all your help! I really do appreciate it.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
how much is required for an investment to double in value if the interest is earned at a rate of 6.25% and compounded annually?
formula to use is:
A = P(1+(r/n))^nt
A is the future amount
P is the present amount
r is the annual interest rate.
n is the number of compounding periods per year.
t is the number of years.
your annual interest rate is 6.25%.
you have to divide the percent interest rate by 100% to get the actual interest rate.
6.25% becomes .0625
this is your annual rate.
the 6.25% is your annual interest rate percent.
you set P equal to 1.
you set A equal to 2 (value of P when it is doubled).
n is equal to 1 because the number of compounding periods per year is set to 1.
r/n = .0625/1 = .0625
t*n = t
t is what you will be solving for.
your formula of:
A = P(1+(r/n))^nt becomes:
2 = 1 * (1.0625)^t which becomes:
2 = (1.0625)^t
take the log of both sides of this equation to get:
log(2) = log(1.0625^5) which becomes:
log(2) = t*log(1.0625)
this is because one of the properties of logarithmic equations is that log(a^b) = b*log(a).
divide both sides of this equation to get:
log(2)/log(1.0625) = t
use your calculator to solve for t to get:
t = 11.433426588
your money should double in 11.433426588 years.
plug that value into your original equation of:
2 = (1.0625)^t to get:
2 = (1.0625)^11.433426588
use your calculator to get:
2 = 2, confirming the value for t is good.
that's your answer.
your money will double in 11.433426588 years at an annual rate of .0625 compounded annually.

Answer by ikleyn(52878) (Show Source):
You can put this solution on YOUR website!
.
Compound Interest formula:
A= P(1+(r/n))^nt

I have to use this formula to answer this question:
Determine how much time is required for an investment to double in value if interest is earned at a rate of 6.25% and compounded annually?

Please give me a detailed answer, I have tried using the formula myself but I keep getting stuck and am not having much success.
Thank you in advance for all your help! I really do appreciate it.
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I came to make a notice to the @Theo' solution.

You may follow @Theo in his calculations to get t = 14.43 years.

But then you must round 14.43 years to the closest integer greater value, which is 15 years.

Only at the end of the 15-th year the bank will make its last compounding,
and it will be first time, when the amount at your account will exceed its doubled original value.

So, 14.43 years is NOT a correct answer in this problem.

Your account will exceed its doubled original value first time after 15 years.

The bank will not make the last compounding earlier than in 15 years.